Hi,
Time is always in seconds. If your PID implementation is non-standard, you are responsible of converting the PID gains to the non-standard time frame used by your PID.
Same goes with the gains. The PID Tuner shows both Integral Gain and Integral Time because in industry either one or the other are standard. So if your PID accepts some custom transformed Integral term, you are responsible for converting it to your special PID form.
I have been working on a presentation that I will officially release soon, hopefully with a video. Maybe this will help you clarify some practical concepts: