As far as I know, the property tax based on reassessment is only increased for the marginal improvement. For example, say I have a house that's currently assessed for $200K, but it's true market value is $500K. I then add a room to the house and the market value jumps to $600K as a result. The new assessed value would be $300K — the original $200K plus the $100K I added by improving the house.

So still undervalued tax-wise, but my property tax increased by 50%.