Property values don't always need to go up in order for taxes to go up. And property values can appear to go up, whenever the entities that be want to raise the property taxes.
Most states have legislation that limits the amount that your homes assessed value can increase, limits the amount the nominal rate can go up, or limits the total increase in your tax burden - or all three
One thing this doesn't impact, though, are local millage increases for things like schools and roads. These aren't covered because they are earmarked for particular reasons, not part of general revenue. Illinois also has a lot of TIF districts that I don't think are covered by this, but I'm not 100% sure because they don't really exist in Arkansas.
Home assessments can be arbitrary. There is no hard rule that guarantees that assessments will be fair. A county can arbitrarily start assessing homes at a higher value if they want more tax income. There have been years where property values barely went up (or lost value) and assessments still increased. ---