Inspection yesterday found cockroaches - advice?

[Ashly B.]

We put an offer on a 4 plex. It meets the 2% rule, has a great cap, all units are rented and honestly needs minimal work (although it has great potential to increase rent with a few upgrades as its in an up and coming neighborhood). When we initially looked at it there is one unit where we were less than pleased with the way the tenants were keeping the place - garbage every where, pets and pee, etc but ultimately we decided it wasn't a deal breaker and when we got the opportunity, we'd raise the rent enough to make it worth it to keep them and we wouldn't be sad if they left. 

Fast forward to the inspection and the unit had visible cockroaches (albeit not a ton, but I know what they say if you see them in the day time... ). We're writing an addendum to the inspection clause that requires the seller to treat that unit as well as pay for an inspection on the other 3 units, and treat them if necessary. That said, its clearly a cleanliness issue that caused them in the first place so how do I deal with the tenant? 

Did some reading here and saw some great ideas like letting them know if the infestation returns its at their expense, but with it being a 4 plex I don't want them to let it go untreated and cause issues for other tenants as well. Would you tell the current owner to evict them? They do have a lease and the tenant has been there 4 years. I don't want to delay closing if I dont have to but also don't want to cause more issues/expense than necessary down the road. Would love to hear how others would handle.