In our county (Riverside) every homeowner got a letter from the assessor's office either revising or leaving as-is. Ours stayed as is, because we've owned the home for 22 years and we're still undervalued compared to current prices.
They do reassess at sale...however, say we bought this month, our taxes would be what they were for the previous owner for the remainder of this year. So we’d be paying the same taxes, the owner would have had, at least till the end of the calendar year.
This can work in your favor if you’re buying a house for investment (which will not have a homestead exemption) but if the previous owners claimed homestead exemption for this year, you get to get in on their rate till the end of the year.
We’ve owned our present home for 20 years and pay relatively low taxes because of a cap that limits the upward assessment to a certain percentage each year. But they only reassess every three years in our county.