PM taking 100% of first month’s rent + 10% of it — is this standard?

I’m trying to understand if a certain fee structure in property management is standard or if it counts as double-charging.

My contract says the property manager gets:

1. 10% of the “gross rents” each month, and
2. 100% of the first month’s rent as a leasing fee when they place a new tenant.

What I’m unsure about is:

If the PM already takes 100% of the first month’s rent as their leasing fee, is it normal for them to ALSO charge their 10% management fee on that same first month’s rent?

For example, if a new tenant’s first month’s rent is $2k: The PM keeps the entire $2k (their leasing fee), and then charges me 10% of $2k ($200) as part of their monthly management fee.

I understand gross rent usually means the full amount charged to the tenant, but I’m trying to figure out whether it’s typical in the industry to use that same month’s rent twice: once for the leasing fee and again for the percentage-based management fee