do you only get houses back if you also chose them

Nope! you can get houses back that you didn't want back. How it works is that at the end of the round with the computer Pi Chi you list the houses you want and your cut list. Say there are 10 houses, you keep 7 and cut 3 to make it simple for this example. Your "keep" list is not listed in preference order; it is in alphabetical order. Your "cut" list is listed in preference order in case you have to go back; #1 being the best of your cut list, #2 being your second least favorite and #3 being your least favorite. So if someone on your "keep" list cuts you but #1 on your cut list invited you back then they will bump back onto your schedule.

So to make more sense of it here are 10 rando chapter at UF:
SK, KKG, Phi Mu, PiPhi, Zeta, DDD, Deeph, XO, ADPi, DZ

So you go through the round and you're like wow! I loved DZ, PiPhi, DDD, KKG, SK, Deeph, and XO. But you didn't really feel it at Phi Mu, Zeta and ADPi. Say you hated ADpi, felt eh about phi mu, and kinda liked zeta but liked other houses more.

So this is your keep list in alphabetical order:
Chi Omega
Delta Delta Delta
Delta Phi Epsilon
Delta Zeta
Pi Beta Phi
Kappa Kappa Gamma
Sigma Kappa

And then this is your cut list in order of preference:
1. Zeta Tau Alpha
2. Phi Mu
3. Alpha Delta Pi


Then say Delta Zeta on your keep list wasn't really feelin it so they didn't invite you back. They drop from your schedule and Zeta bumps back onto your schedule if they invited you back. It will keep going until you run out of houses.