Soaking wet and plated in gold, assuming it's all 100% true as they are leading on, it's pathetic that a man, native Californian, no less, closer to 60 than to 50 years old, is so naive and inexperienced about real estate.
They just don't have the air of people who have just completed a home purchase, let alone their first one.
My impression of what occurred, based purely on speculation and tea-leaf reading, and my own not unsubstantial experience and expertise in real estate and real property law, is that his mom owns that place, and it was rented for less than the rent she was coughing up monthly for their Anacrapa Cabana. The tenants vacated. Mom figured it was a better financial deal for her to pay herself rather than to keep throwing money down the Irvine Company rathole for their stupid apartment. So Mom took out a token mortgage on the joint, and that's what she is referring to as "when we closed". And the Mom's idea is probably that KT and Spin-Sir will cover the mortgage and carrying costs. And that will never happen.
We hear much more about KT's family than Spin-Sir's. Is it possible that she owns at least part of the Malibu apartment building? Their "new furniture" looks like the kind of stuff you would put in places like that to rent as "furnished", especially for short-term rentals. If so, good for his mom! But Sit-and-Spin-Sir sure has a long way to go and to grow before he can step into Mom's shoes.