I read up on my phonology, and I found that, instead of the pronunciation of a word like "сімдесят" being something like "simdesʲjat" (deliberately approximate), and a word akin to "дев'яносто" being "dev janosto," it's actually "simdesʲat" and "devjanosto." Is this correct?
Yes, я, ю, є after a consonant usually is not pronounced ja, ju, or je. It just palatalizes (the small J) the consonant and says a, u, or e. Unless it is preceded by an apostrophe, in which case it does not palatalize the consonant and is pronounced fully. Labials (м, п, в, б, ф) are never palatalized, so they pretty much always get an apostrophe before one of these letters.