And this is CRE, so it's cutthroat, it's no one's problem but your own if you lose an earnest money deposit. 

Should I have them pay right now or out of security deposit whenever they move out? 

Which is why there is more investment in real estate and bank deposits  in the “western world” (which includes.

If a buyer is coming down with a high-down payment and quickly making a large deposit into escrow fighting tooth and nail about proof of funds may be a red herring.Credibility is also a factor here.

Others will collect first, last, and a smaller deposit.

Deposits were in my account. 

I'll reach out to the lawyer in the meantime, but I suspect if they refuse to pay it, it'll have to come out of their security deposits when they move out?

At a bare minimum, I would require a written lease agreement and a standard security deposit equal to an entire month of rent.

So the total amount that should be paid will be rent for remaining days in month + security depositORrent for remaining days in month + next month + deposit - I don't know when would this situation arise.

Ideally, you'll want to see average 90% occupancy across the board, otherwise you'll be relegated to regional bank and credit union lenders that require (i) recourse, (ii) deposit requirements at close, (iii) slightly higher rates, (iv) lower amortization, and (v) less interest only [if cash flow is a priority for you].