Hi,
Yes, it seems you need to modify the gains as you suggest. Also it seems your implementation does not have Derivative action, so when you choose a model in de pidtuner app, make sure is a first order model as to make sure Derivative action is zero.
Take a look to this presentation if you want more confidence that you are doing PID tuning correctly:
https://github.com/pidtuner/pidtuner.github.io/blob/master/assets/doc/PID%20Tuner.pdf