Terminology matters here. You refer to the entity that receives the rent as your "agent", and not as something else, such as a rental property management company that you pay.
Your agent acts on your behalf and is therefore identified as being "you" when it comes to taxes. So when your agent receives the rent, it's treated exactly the same as if "you personally" received it on that same date. The income is therefore reportable in the tax year it is received, weather it's your agent that receives it first, or you.
Now if you pay a rental property management business to manage the property for you, that would mean that you do "not" actively participate in the management of that property. In other words, the property management entity makes all management decisions for you, on your behalf and in your best interest. Things like determining who qualifies to actually rent the property to you, as well as taking care of repairs and any other maintenance on the property needed. With this scenario, the term called "constructive receipt" comes into play. The money is reported in the tax year you have control of that money.
So if the management company receives the payment on Dec 30th, but you don't have actual access to and control of that money until Jan 2nd of the next tax year, then it's reported as income on your tax return for that next tax year, and not the tax year the management company received the money.
Now let's sayf it's a case of where the management company mailed you a check that was dated say, Dec 30th, and you didn't receive that check until Jan 2nd, the management company lost their control over that money on Dec 30th - the date of the check and the day they dropped it into the mailbox. Therefore, you would have "constructive receipt" on Dec 30th of that prior tax year and where therefore include it in your income for that prior tax year. In this scenario the management company would be correct in including that amount in any 1099-MISC they issued to you, reporting rental income paid to you in that prior tax year.
