1st month's rent last month's rent??

I'm interested if anyone has insight?? Recently put a rental security deposit on a luxury unit in a building on the N side of Williamsburg. The unit is currently occupied & the tenant is breaking his lease - so that's how the unit became available. The broker is asking for first month's rent, last month's rent and also a security deposit of one month's rent to move in. But the unit is occupied??? That tenant moves out may 31 and I move in June 1. I've never heard of paying "last month's rent" for a luxury unit that will be occupied for that month. Just curious if anyone has had experience with this. I'm getting too old for all this! Been in Manhattan for 12 years - this is my first apt in Bklyn - but the whole city seems to be getting shadier and shadier ...