Nathan - if you paid $0 what was the consideration to acquire the property?
Whatever consideration you paid was the purchase price of the real property, personal property (if any), and any accounts payable/receivable - unless those were explicitly excluded from the purchase.
Therefore, if the purchase price came with the security deposits, and the security deposits (or any portion thereof) do not need to be refunded, they may not be income to you.
It may be possible that those funds will adjust your cost basis. It may be possible that those funds are compensation for fees/services rendered. It may be possible that the money is classified some other way.
Just because the money is new to you doesn't necessarily make it taxable income.
btw - when income is realized depends on your accounting method. If you use cash accounting, income is reported as of when it is actually received by you and expenses are reported as of when they are actually paid by you. If you use accrual accounting, income is reported when it is obligated to be paid to you (whether or not it is actually paid - if it is not paid, it gets deducted as writing off bad debt), and expenses are reported whenever you are obligated to pay them (again, whether or not you actually paid it - however, if you never pay it, they can't be used as a business expense to offset income.)