What exactly does a resistor's tolerance rating mean?
A decent manufacturer will specify pretty clearly in the datasheet what is meant. For example, here's the relevant table from one vendor I've used:



As you expected, the resistor tolerance is the limit on the resistance at 25 C, and the variation over temperature is covered by a separate TCR specification.

But remember the resistance can also change due to other environmental factors, such as prolonged operation at high or low temperature, operation at high voltage, mechanical stress, etc. If any of these stresses is applied to your device you could see its value vary from day to day, with the value at 25 C remaining within the specified tolerance limits.