As far as TOT, I am not in San Diego so I won't guess an answer for that part of your question. If SD is anything like my area, they don't care *who* pays it, so long as it is paid. Legally, if you collect and then no one remits you're in deep doo doo, so I'd definitely make sure your friend passes it along
What's missing from your question is: what does "manage" include for your friend's place?
From the law for TOT:
“Operator” means the Person who is the proprietor of the Hotel, Recreational Vehicle Park, or Campground, whether in the capacity of owner, lessee, sublessee, mortgagee in possession, licensee, or any other capacity. “Operator” includes a managing agent, a resident manager, or a resident agent, of any type or character, other than an employee without management responsibility.
Generally speaking, the Operator is going to be the person who collects the money and makes the decisions about who to rent to.
I have managers whose sole responsibility for the guest is to handle anything bad that happens during their stay, they don't collect money, so they aren't the "operator", that title would stay with me still.