Landlord wants to move into my rental

I have lived in a rental for approximately 8 years in California. I signed a new lease on Jan 1, but the Landlord changed his mind and didn’t sign. He said he is retiring and wants to move back to Temecula. He served me with a 60 day notice to quit. I told him I couldn’t come up with a new deposit and first months rent to move into a new place in 60 days. I asked for more time and he said no, because he had to get repair personnel into the house and gut it to repair persistant plumbing problems as soon as possible. I then got the financing and got out in 30 days and then I called the property manager and told her we were out so they could go ahead and get the repair people in. I spoke with the landlord and I thought everything was settled. Approximately 5 days later, I received a 3 day notice to pay rent or move out. It was forwarded to my new address. I didn’t know what was going on. Then I received a notice of filing of an unlawfuld detainer complaint. Since we have been out for over two weeks, I didn’t understand. I called the landlord and he told me he was doing an unlawful detainer because we moved out in 30 days instead of 60 days and I owed him for March, even though we moved out on March 1. It was my understanding he wanted us out ASAP, but sent the 60 day notice because he could not by law, make it 30 days. Am I responsible for the month of March?