“However, if you improve the home (other than normal repairs or maintenance), the tax ceiling may go higher because of the new additions. “
If your house appraised value goes up or the tax rates go up your taxes will go up!
The key is not to make any major improvement to the property after you have been locked in (an addition, ect).
You buy something very new, or very recently renovated just prior to turning 65 that might even be under valued on the tax rolls... then apply to lock in the current rate as soon as you turn 65 and then dont make any major improvements to the property which will reset it.
here is an article about how the freeze is affecting cities budgets:
https://www.dallasnews.com/news/news/2010/01/17/Property-tax-cap-for-seniors-puts-8031