Getting a burst of more-modern recruitment the turn after you unify is really common. Usually, I see vassals make more of my stuff than protectorates, and if they'd deployed more of their stuff outside their city before becoming vassalized, they make more - but they also seem to make some outside the city sometimes. I'm pretty sure I've taken over minors who had more than 20 militia units in their city, too, so even that might not be a hard-and-fast rule (which, yes, would be very weird given how hard-and-fast the stack limit appears to be in the rest of the game).
As to what units they pick, as long as you have some 30-turn-old design for a given unit type, you shouldn't see any militia/irregular/raider/etc units in that slot. They won't always pick the newest designs, though, and I don't see a rhyme or reason to it. If I don't have pressing model design tasks, and I have a dead-end design that I'm not using (forex if I had a terrible starting structural design unit that I replaced), I'll periodically update these designs just so there's more and better obsolete models available to chose from. That's a luxury for when your MD council is competent but you're not getting tech/testing to merit constant modern design updates, though.
Cults are poorly documented, yeah. Like, there's no clear indication of the downside of various cults, so you might not even know what they're doing unless you dig through the reports. E.g., Anima seems pretty benign for the most part, but they also harass any of your leaders with high egoism and reduce your relation with them. Vic said this week that there'll be a major manual update when the DLC comes out, so hopefully the Cults/Corp/useless trash modules will get proper documentation then...
[Oh, yeah, that link is VERY nice, thanks Karlito!]
[And on the subject of "weird recruitment things that make no sense", I had alien mercs hired from a zone three hexes from the north pole show up in the isolated vassal that Hornstein's overrunning... 7 hexes from the south pole...]