During a 15 minute soak in my digital kiln

The soak should hold the kiln at a temperature for the length of time that you programmed. The temperature may keep climbing a little, however, at the beginning of a soak if the soak was preceded by a fast temperature climb. This is called temperature overshoot. After a few minutes, the temperature will stabilize. You might also be seeing temperature fluctuation during the soak period. This may not indicate an actual change of kiln temperature but rather a change in the temperature readout. Temperature fluctuation could be due to a loose thermocouple wire. Current-carrying wires that are too close to the controller or the thermocouple wires could also cause temperature fluctuation. A relay that is stuck in the "on" position can cause the temperature to rise during a soak.