I think you're talking about crosslinking latex paints.
(Lemme explain this.)
Crosslinking latex paints (like latex floor paints) will typically take up to a month to fully cure, but most latex paints don't crosslink. Typically you find that the higher quality interior latex wall paints and ALL latex floor paints (where hardness is most important) will have acrylic binders which crosslink, but most latex paints form a film through a process called "coalescence". That is, most latex paints stop at "coalescence". Crosslinking latex paints go through that same coalescence process to form a film, but then also form chemical linkages within that paint film. The coalescence both kinds of latex paints go through is a physical transformation that doesn't involve any chemical reactions at all. Only the crosslinking latex paints have chemical reactions in that secondary crosslinking part of their curing process.
A normal latex paint consists of a SLURRY of tiny hard clear particles of either white wood glue or Plexiglas and solid coloured particles (called "coloured pigments") and solid white or clear particles (called "extender pigments") suspended in a solution of water and low volatility water soluble solvent called a "coalescing agent" or "coalescing solvent". So, 5 things; hard clear plastic binder particles, solid coloured particles and huge massive rocks almost large enough to see with the naked eye all suspended in a mixture of water and a slow to evaporate water soluble solvent... that's primarily what's in a can of latex paint.
When you first apply the latex paint to a wall, the first thing that happens is the water in it starts to evaporate. As a result, the tiny clear hard plastic particles (called "resins" or "binder resins") find themselves surrounded by the coaleascing solvent at an ever increasing concentration. The coalescing solvent dissolves into those hard clear binder resins making them soft and mushy. Then, the same forces that cause tiny water droplets to coalesce into large drops of rain inside the clowds (capillary pressure and surface tension) also act to cause these soft mushy resins to coalesce together so that you end up with a continuous film of soft mushy clear plastic with the coloured pigments and extender pigments suspended inside it very much like raisins in raisin bread. Then, as the coalescing solvents evaporate out of the paint film (and you begin to smell that "freshly painted smell" in the air which is in most cases a solvent called "Texanol")), the clear plastic hardens back up again to the same hardness it was before that film formation started, and the plastic consisted of tiny clear hard particles in suspension in a liquid.
The above is what MOST latex paints do to earn a living. Once the coalescing solvent evaporates from the latex paint, filling the room with that "freshly painted smell", then film formation is complete, and that latex paint won't change at all (except that the glycerine added when tinting the paint will still evaporate from it, but that won't change any of the paint film's properties significantly).
A cross linking latex paint will go through that same film formation process, but then chemical bonds will form between reactive groups on the surface of the resins, and those additional chemical bonds that form between neighboring resins act just like a roll cage in a racing car, making the film harder (if you were to squeeze it) and stronger (if you were to stretch it).
In both a regular and a crosslinking latex paint, coalescence only takes one to two days and film formation is complete within 3 to 4 days. (Film formation is only complete when the plastic film is as hard as it should be, and that only happens once all the coalescing solvents have evaporated.) It's that additional crosslinking that goes on after film formation in crosslinking latex paints that will take up to a month.
Typically, the top of the line interior latex paints will use cross linking resins because those paints will ALSO use very hard extender pigments (like pulverized silica sand instead of chaulk or talc). If you want a paint to stand up to hard scrubbing without losing it's gloss, then you have to make the paint with BOTH hard extender pigments and a binder that dries hard and strong. Having hard extender pigments in a soft binder will result in the hard extender pigments being rubbed off the paint film and won't work any better than having soft extender pigments in a hard binder as both will be worn down by scrubbing. You need both the extender pigments and the binder to be hard and strong for the paint to stand up to hard scrubbing. So, in top quality paints, they'll use a very hard extender pigment (like pulverized silica sand) and the hardest and stongest latex binder resins you can get, which are the cross linking ones.
And, of course, on a working surface like a floor, hardness is paramount in importance. The harder the floor paint, the less it will be damaged by foot traffic, and the longer it'll stay looking new. So, every paint company will use it's hardest drying paint to make floor paint. Unfortunately, latex floor paints will be made with crosslinking acrylic resins, but still won't be sufficiently hard to provide the same level of performance we've come to expect from oil based floor paints.
You can learn more than you need or want to know about latex paints (and a little about oil based paints) at the Paint Quality Institute's web site at:
(To get to the good stuff, click on the Media Center link next to the red Home link. Then click on the PQI Publications link to get to this page:
Download and read the two PDF files entitled: "The Ingredients of Paint and Their Impact on Paint Properties" and "How Colour is Affected by the Ingredients of Paint". If you read and understand those two brochures, you'll know more about latex paints than most people that work in paint stores.)
The Paint Quality Institute was established by the Rohm & Haas Company, which, until they became a subsidiary of Dow Chemical, were the largest manufacturer of the plastic called "polymethyl methacrylate" in North America. You probably know that plastic better by the name "Plexiglas", "Lucite", or "Perspex", depending on which chemical company made it. Polymethyl methacrylate is the plastic used to make binders for top quality latex paints, so using a top quality latex paint will result in a film of Plexiglas on your walls! Lesser quality or "budget priced" latex paints will use a different binder made from a plastic called "polyvinyl acetate". Polyvinyl acetate is also the plastic used to make white wood glue, and in fact many of the problems associated with using budget priced paints are associated with the fact that white wood glue has a very low resistance to moisture and humidity. Elmer's white wood glue, polyvinyl acetate concrete bonding agents, acrylic nail polish, acrylic grout sealers, acrylic floor "wax" and acrylic (or "latex") caulks all use that same "coalescence" film formation process described above that latex paints do, although they the resins used to make a glue or a caulk or a nail polish will be different from the ones chosen to make a paint. In the paint manufacturing industry, paints made with polymethyl methacrylate (Plexiglas) binder resins will be called "100% Acrylic" paints, whereas paints made with polyvinyl acetate resins will be called "Vinyl Acrylic" paints. However, there are hundreds of different kinds of "100% Acrylic" and "Vinyl Acrylic" resins each with it's own characteristics, so don't think that the wording "100% Acrylic" on a can of paint means that you're wasting your money buying a more expensive paint. "100% Acrylic" on a can of paint means exactly the same thing as "100% Cow" on a package of meat does. What's inside might me prime rib or dog food depending on WHICH acrylic resin the paint was made with.
In the case at hand, it's doubtful that any paint made specifically for use in bathrooms would also use a crosslinking latex resin. That's because the resin they'd choose to make a bathroom paint would be chosen according to it's resistance to moisture and humidity, as well as how mobile the mildewcide would be in that binder. So, hardness and scrubbability wouldn't be important considerations in picking a binder resin for making a bathroom paint. (How often do you clean your painted bathroom walls and ceiling?)
If the original poster were to use a top quality interior wall paint instead of one specifically made for bathrooms, then you'd be correct in telling him it'd take up to a month to fully harden (cuz it would probably use a crosslinking binder). A bathroom paint will use the binder most resistant to moisture and humidity, not the binder that forms the hardest film.