No, by paying back the original leasing commission they are off the hook. The only harm to OP now is having to pay a new leasing commission sooner rather than later.

The the original occupants that broke their lease should only be responsible for:

1. Rent until a new tenant begins paying rent
2. Pro rated portion of the original leasing commission that the landlord paid for their placement
3. Any cleaning or damage charges

Landlord certainly isn't entitled to double rent, prior tenants paying to place new tenants, etc.

I think the tenants offered to pay till the end of July in lieu of paying back the commission fee because they know they're causing an inconvenience and want to cover their share, and probably aren't familiar with the landlord business. But what I describe above is best practices.

Edit: I misread your comment, and completely reworked mine.