In other words, don't be nit picky, allow them the freedom to live there much in same manner as they could if they owned, after all that is what you leased, owner's rights of possession.

The tenants have until May 31st to move and I regain possession on June 1st.

I had another thought - if I was you, I would email him and tell him that you do not want photos of the interior of your apartment that show your personal possessions made public in any way, because you are concerned about someone burglarizing your home.That way, he can't just post your personal possessions on realtor.com or Craiglist with the address to where someone can find you lovely, expensive MacBook Pro, for instance.And then if you are burglarized, he gets to pay your renter's insurance deductible, since you forewarned him of your concern. 

He took possession Feb 1st, and has had no problem until today. 

This means, that if a tenant breaks a lease, you're required to try to find a new tenant asap using reasonable means, and can only continue charging the tenant rent until you get a new tenant in the unit.But, this does not give you the right to take possession before they have defaulted, in my opinion. 

I might call the previous tenant myself and ask if they would return the package I know they have in their possession. 

That's for possession of the property.

So why am I on the hook for any of his other actions or possessions anywhere else?

I won the judgement for possession yesterday - now patiently waiting for the automatic 10-day appeal period to expire to file the writ.  

If so,  did you ask the court for possession and rent owed ?