If you look at the video series on PID I’m putting together on YouTube I go over the Dependent form equation. Have a look at it: ControlLogix PID Essentials
If you look at the Rockwell variant of the dependent PID equation:
It is clear that Kc = Pgain is a multiplier of the other terms and that Tau_i = Igain is in the denominator in the integral component. Meaning the smaller the Igain value you set the larger the Integral component. This is not the case in the Independent equation as Ki is in the numerator. That said, with the Pgain value you have of < 1 you are essential multiplying the Integral term by a fraction or diminishing the Integral component because Kc (which is the Pgain you are setting) becomes a scalar or multiplier of the error, I and D terms.
I hope that helps!