Most residential managers will handle voucher units, and the fee is usually the same percentage they charge on market units, commonly somewhere in the 8 to 10 percent range. Some add a separate leasing fee when a new voucher tenant moves in, because the paperwork front end is heavier than a market lease. Ask your guy directly whether he has units under a HAP contract now, meaning a Housing Assistance Payments contract, which is the agreement between you as owner and the public housing authority that says how much they pay you each month. A manager who has never signed one will learn on your unit.
On the two things you were told, the ongoing month is light. The housing authority sends its portion by direct deposit, so there's no chasing that part. The heavy months are the front end and the annual recertification, when the authority re-checks the tenant's income and can change the split between what they pay and what the tenant pays. Your total rent usually doesn't move at that moment, the shares inside it do.
The part people miss is the inspection. Your unit has to pass a housing quality inspection before any payment starts and stay in compliance after that. A manager earns their fee here by knowing what the local inspectors flag, since the standard is federal but inspectors are local people with local habits. Ask him what the last three fail items he saw were. If he can name them, he's done this. If he says it's straightforward, keep asking questions.
