Yea they can and will get you. My current home, taxes were 1900 when i purchased it. I was like sweet, that's a deal! Got one year with that amount, The following year tax literally jumped to 3500. The assessed value went up 70%. And i did not put 70% of improvements in (yet, i have now + a ton more).
And i'm nervous for the next tax year. We did big upstairs remodel recently. City's property assessor knocked on my door a few weeks ago asking to get in to view it. I said no, and he was like well, if i don't get in we may end up valuing your property for more than its worth. I did a high end remodel, so i doubt it will come in over what the place is really worth. So I took the gamble... But I know i'm going to be paying more soon!