I think is called burnishing the tape. Go over the tape w/ a narrow putty knife to press it down tight to the surface and follow all of the contours of the texture. This is imperfect at best. I would bet you still end up w/ paint "wicking" under the tape.
Probably your best option will be to get really good with a cut in brush. Get a HIGH QUALITY 1" beveled end brush and start practicing painting right up to the edge of your trim, corners, etc. Unless you are completely unable to still a shakey hand, you'll be surprised how quickly you will get the hang of it and be able to paint right up to a piece of trim without actually getting paint onto the trim. If you use latex paint, you will also be able to wipe off any little mistakes with a wet rag right away.
I'm sure others here can give you pointers on the technique. I've managed to get good enough for my needs on my own, so I don't really have a good description of how I do it, I just do. If that makes sense.