Let's say the seller bought the house years ago for $X and his yearly property taxes are $1,200 - or $100 per month. You buy the house for twice as much as the seller bought it for and close escrow 2 months before the next tax bill is due. Since the seller already paid taxes for two months, you reimburse the seller $200 as part of the closing costs at time of purchase.
But wait! Since you bought the home for twice as much as the seller paid, your assessed value is twice as much. Therefore, you actually owe $400 for those two months. This is where the stupidity kicks in. You should be able to reimburse the seller for the $200 they already paid plus pay the county the additional $200 and be done with it, but NOOOOO. That would be too easy. Instead, the county must have a complete department preparing supplemental bills and processing them - a complete waste. I'd gladly support any ballot proposition that requires mandatory prison sentences for government officials who allow this system to continue.
One other clarification: you may get supplemental tax bills in the future if the county re-assesses your property to a higher value.
Thankfully, I'm sure, the supplemental tax is a one-time adjustment to cover the increase in value of the property brought about by your purchase.
After this, valuations are based on the County Assessorâ€™s valuation (which can be challenged via a Prop 8 Appeal - see blog post below, also see the supplemental tax paragraph that touches on how the buyer "adopts" the seller's tax basis for a short time).
"Estimating Property Taxes in CA"