When I was full-time onsight our lease had an addendum that stated the apartment has been inspected and is bed bug free. The resident(s) sign that document. If bed bugs then appear, the resident(s) pay for treatment. So that is a yes!! If your lease doesn't have such an addendum, consult your legal and get one.
The first time, no. We want residents to be encouraged to tell us so that we can inspect other units and treat properly. If it persists or they do not prepare appropriately, then yes.
Multi family you really can’t as you can’t determine conclusively they were the cause. Unless you are a bit sketchy and try to offload all your unknown caused expenses to your residences.