Legal Question in Landlord & Tenant Law in California

You are correct not to pay the former owner and to demand your security deposit back. The good news is that the bank is jointly and severally liable with the landlord for the deposit now that the bank owns it and your deposit has not been refunded. Yes, if the bank has given you notice to vacate you have 90 days from that notice. If your lease expired later than that, you would have until then, but since your lease expired today, you have 90 days from the notice. In order to remain entitled to that notice, however, you do need to pay rent to the bank. By law once your lease expires your rental becomes a month-to-month tenancy unless something occurs to terminate it (in this case the 90-day notice you received). So the bank is now your landlord under the terms of your old lease, and it is the same as if you were any other month-to-month tenant who had received notice terminating the month-to-month tenancy, only you get more time.

So what you should be doing is finding a new place to live. If you find someplace to move into sooner than the 90-days, you can give 30-days notice if that will expire sooner than the 90-days, and then your rent obligation to the bank will only run until the 30-days is up.