Would anybody know?

Zerenity • 28. Arizonan. Army Wife 💍
Okay, so I just got done settling a huge debt of about $900 from a place I was a co-signed on with my ex in 2016. So far it hasn't updated my credit report ( I know it can take 30-60 days for an update) but when I go to apply for let's say an apartment of my own, do I have to put this debt down since it was for a previous apartment? I know you shouldn't lie on an application because if they find out and you didn't tell them you could be turned down for it and also an inquiry on your report that really you don't want. So this leads to my question. They see the debt on there through the creditor, then the original creditor, are they allowed to call the debt collector for details or the original property manager as to what happened? 
I'm just curious because I don't want somebody having my information what so ever. I do have the copy in my hands saying I am no longer liable for the debt and it's satisfied in full. Sorry for it being so long and so many questions this is my first time doing something like this. Thank you. 😊😊