Increased assessments does not mean increased taxes .
Most of the time, it does mean increased taxes. They are not always proportional to the increased assessments. BTDT.
I have filed appeals, and usually gotten an automatic reduction of 5-10% in the final property tax (after it was increased). The folks in the assessor's office simply want people to go away and won't contest a minor reduction.
I suppose that if one attempts a large reduction from the appeals process, the clerks may become vindictive and increase the assessment even further. I haven't pushed those limits.
Then there was our county commissioner who owned a residence assessed at 4% of fair market value for over a decade. Just a minor oversight from the assessor's office, I guess. Or a private version of "Proposition 13". That deal was not available to me or anybody else. A lot of people asked about it, and the clerks were instructed not to discuss the matter.