"should that be the tax id for the Property Manager since they are collecting income and will send a 1099 to me"
Most likely, yes. AirBNB needs the tax ID of the person or business that they pay the rental income to. So if rental income is deposited in/paid to an account with your name on it, that would be your tax ID they need. My response is based on rough information, as I don't know the detailed set up or arrangement between you, your property manager and AirBNB.
