No, the tint formula for a paint will be specific to the particular paint manufacturer and will only be "right on" for that manufacturer's paint. Your best bet would be to find out what Benjamin Moore colour that tint formula applies to, get a sample chip of that BM colour, and give it to Mills paint to duplicate.
You see, the first thing that's going to make a difference is that each company's "white" tint base is a different colour. Paint tint bases only look white when you've got nothing else to compare them to, but just like different sheets of white paper, they'll all be different shades of white when compared side by side. So, tinting someone else's tint base will result in a similar, but not quite right, colour.
Also, every different paint manufacturer will have it's own paint colourants, and these won't always match. For example, if BM uses an orange colourant in it's tinting machine and Mill's doesn't, if the tint formula calls for some of that orange colourant and Mills paint uses a mixture of yellow and red instead, then the two paints might end up being visibly different.
Also, different paint companies will use different pigments in their colourants. There are a half dozen different red pigments and another half dozen different yellow pigments being used to tint paints, and each different red or yellow has a different hue.
So, get a sample chip of the BM paint your tenant likes, and get Mills paints to reproduce that colour with their tint machine. With the colour matching computers they have now, they should be able to do that without a problem.