A lot of this is dependent upon some of fine print in the PA, and you're agent should be able to answer the questions with regard to who is responsible for what, so I don't want to speak too much to that.
More so, I'll speak to what is "normal," at least in our market. Especially when the seller is a primary homeowner, that occupancy is common. We see it up at 60 days occupancy a lot of the time, too. And, it is often also that FREE occupancy I think you're referring to here. Basically, they are responsible for all utilities, however, the taxes are prorated beginning the day of close and you are responsible for mortgage payments if there are any before occupancy ends. Most likely, this occupancy really is what got this under contract for you. If you didn't do it, they would have found someone else who would have.
Another win here might be that you won't even have a mortgage payment before they move out. If you close in June, your first payment isn't until August 1st.