I read your earlier Post and decided not to respond because I haven't lived in California for decades.
But since you didn't get a response from someone who knows what they're talking about, I'll offer something to think about.
Around the Country, One (1) months rent is typical compensation for a LandLord to pay a Rental Agent to find a "Good" Tenant. That includes doing some rudimentary background and credit check to make sure they are not a deadbeat.
In your case, the LandLord is going to perform his own Tenant background checks, et cetera, while your own Agent has not been involved at all in this property. Your Agent may not want to take on the responsibilities that you want addressed, nor does their E&O Insurance necessarily cover those activities unless they are commonly engaged in.
Handling your money and, these days, verifying that it is a legitimate Rental, and that the entity purporting to be the Landlord actually owns the dwelling, may be more difficult a task to perform than doing the background check mentioned earlier on the Tenants; and these scams are more sophisticated.
I di as few rentals as possible. As cut and dry as your situation appears on the surface, I personally wouldn't want to get involved vis-à-vis the risks involved . . . . but your Agent may do this all the time. Maybe your Agent will do it as a Friend, and in return for potential future business. Anyway, One Month's Rent would be a reasonable starting point.
There, now someone else can say I'm off the wall.
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Dale C. Hittle of GOLDEN RULE PROPERTIES in Glover, Vermont
Where We're Always Striving To Put Together "THE FAIR DEAL"