Not sure what you mean here Joec.
Basically, the assessor should not value any property higher than its market value. If they are too high, you can appeal and get it lowered. You have to justify your appeal with comps, etc. and make your case. If you just bought a property in a free and open market transaction, that should be a pretty convincing argument. Once the assessed value is lowered, the assessment should stay low if the real market value stays low.
However, once the market demonstrably recovers, the assessor has the right to “catch up” by raising it accordingly, even if by more than 2% a year.
The limitation of 2% a year increases under Prop 13 uses as a benchmark your original assessment. Once the catching up phase is done and the assessor hits the 2% per year limitation, Prop 13 will protect you from big annual increases.