The Integral Gain (also called Integral Time) determines how much impact the error-over-time has on the calculated output signal. It's not how often the Integral Error is added to the calculated output.
The Integral Error is constantly being added to your Proportional Error to make up calculated output signal. Your Integral Error is the constantly running sum of your Proportional Error divided by your Integral Gain (also called Integral Time).
I attached a page from a CVAHU, that shows some default PID settings-
Default PID.pdf
But the CVAHU uses Control Bands. Where as the XL15C uses Deadband(Percentage of Throttling Range) and deadband delay.