if “alien” sites are down, then the subs will tend to reselect neighbour cells. But if none is available, then they will (wildly) look for a cell from a different PLMN (= yours).
You can’t avoid this. The best for you would be to do a roaming agreement and accept those incoming visitors. As soon as their site is up, they will camp back on the home PLMN.
(note : this scenario is just an assumption ! i’m not saying it is what’s happening.)