Suspicious PM Actions?

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Hi Everyone,

So we recently rented out one of our rentals and the tenant moved in on 8/1. Before they moved in they handed the August rent and non refundable pet deposit to the management company on 7/31. When I went to check my online portal on Monday, I noticed the PM charged their management fee for July based on the total amount of money received, meaning the rent and pet deposit combined. 

So 2 questions here:

1. Even though the pet deposit is non refundable, and can be counted as income the minute it was received, why do I have to pay the PM a percentage just to receive that deposit and to the tenant I still have to say I have the full pet deposit set aside when they are ready to move out?

2. Even though the rent was received on 7/31, the rent the tenants paid really isn't due until 8/1, is it right for the PM to charge that fee in July, when for the entire July month the house was basically vacant?

This is a new PM that I inherited from purchasing the home, and I have had a lot of issues with them. We have another rental with another PM and they don't charge a percentage for the pet deposit we received from the tenant. Maybe the above points are all normal and I am just being suspicious about their operation, but any input would be greatly appreciated.