It has nothing to do with the volatility of income tax revenues, but it has everything to do with volatility in the budgeting process. By gutting the ability of local governments to fund themselves it pushed all of the taxation up to the state level (and the state turns around and hands most of the money back to the local jurisdictions.) Since the primary revenue generators at the statewide level are income and sales taxes this introduces volatility that is directly tied to the general economic condition, unfortunately the new burdens placed on the state budget as a result of Prop 13 are mostly independent of the general economic condition. This lethal combination leads to a never-ending cycle of boom and bust in the state budget.
Prop 13 doesn't make state-level taxation volatile.
Taxable incomes haven't dropped by 50% in CA. What has dropped is the taxable incomes of the small fraction of CA folks who pay the bulk of CA's income taxes.
CA's income taxes are very progressive. That makes them very volatile.
Prop 13 has nothing to do with the volatility of CA's income tax revenues.