Is this something I can deduct from their security deposit if there is more damage due to them not notifying me immediately? 

She had a choice of putting down a deposit equal to two month's rent or paying monthly "deposit insurance." 

., 1 year)]Security Deposit: [Enter the amount of the security deposit]Background and Credit Check: [Indicate whether applicants will undergo a background and credit check]Rental Application Fee: [Mention if there is an application fee and its amount]Don't miss out on this fantastic opportunity to make our lovely single family home your own!

Best use of this "extra" money has seemed to be for paying down payment of 3 additional homes per year at the 70-90k price range. (15-20k deposit each, 5-15k repairs each, additional cashflow avg 320/mth each).          

I see it has an area for fees in lieu and an area for security deposits.

The mortgage market is healthy so there are several ways for income to be calculated including but not limited too: full income verification of two years W-2's or tax returns, 1-2 years of a 1099, average deposits of 12-24 months of personal or (50%) of business bank statements, an up to date P&L, DSCR (debt service coverage ratio) or rental income (investment properties only). - Appraisal.

If you're worried about damage, I think some form of security deposit for longer stays makes sense.

. - Higher and Hard Deposits.

I have my tenants deposit everything into my predesignated back account. 

If you are paying in cash, you'd have the bank write a letter indicating you have the capital on deposit or you can also print out your bank statement showing the funds.