Ok, everyone has a different answer for this question, but I think the bottom line here for the Original Poster is that the answer to your question entirely depends on #1) What insects they are spraying for and what chemical(s) they will be spraying, and then #2) Talking to not only the exterminator company that's spraying the apartments every month (they are being paid, I wouldn't just take their word for it if they say "Oh yeah, they'll be fine in an hour or two"), but WRITING DOWN What insects/rodents they are spraying for (not only are the chemicals dangerous to your birds but also possibly the critters they're spraying for), Exactly what chemicals/all ingredients are in the stuff they'll be spraying, and lastly What quantity of spray will be sprayed in each room during each treatment, where the stuff will be sprayed (what surfaces/areas), and with what exact frequency. After you get the answers to all of these questions from the SPECIFIC company that the apartment complex has hired (do not take "I don't know" for an answer on these questions) and you've got them written down, you need to take these answers to a certified avian vet, Hazmat/environmental health agency, or an environmental protection agency like EPA or DEP (the certified avian vet is best) and ask them what they think you need to do after EACH of these treatments, how long the birds need to be out of the apartment each month after each treatment, is it even going to be alright AT ALL for them to be in the apartment after doing these treatments, their suggestions about cleaning the chemicals off the surfaces that have been sprayed, and if the insects/rodents or whatever they're spraying for monthly (they must have an issue to spray each apartment monthly) also poses a threat to your birds!
You can't just say "Yes, your birds will be fine", "Yes, just take them out for a couple of hours", "Oh yeah, they sprayed our apartment and we took the birds out for the day and they were all fine. Your birds will be fine, just do this because we did this and it what OK", etc. All companies are spraying for different critters, all companies use different chemicals, they all have different procedures and policies for spraying living spaces, etc. So this is NOT a situation where someone else's prior experience is good enough.
This situation is unique in every instance and you need to find out the answers to all of the questions I listed from a certified avian vet or environmental health professional BEFORE you move your birds into that apartment. If they've been spraying those apartments prior to you moving in (possibly for a long time) you don't know if the chemicals they use build up not only in the air/duct work but more importantly on the walls, carpets, and all surfaces in the apartment. If they use chemicals that are toxic to your birds just by your birds being in physical contact with them, then you could potentially harm your birds just by moving them into the apartment and letting them walk on the floor.
Bottom line is you need to get the exact specifics from the exterminator company the apartment complex is using about what they spray, where they spray it, how often they spray it, and what they are spraying for. Then take this info to an avian professional. Each situation is going to be different and our prior exterminator experience is not good enough in a potentially fatal situation your birds will be living in monthly!
Sent from my XT1575 using Tapatalk