Yes, that's the tip detection routine, before reading the TC it outputs a very short pulse.
Normally it's barely noticeable, but reducing ADC time will make it noisier.
If you added a 1M resistor between Heater and 3.3V (Or 10M across the MOSFET drain and source) then you can disable the "Active detection", noise will go away.
Also, now it's working you can try lowering the ADC time back to 200ms, then lowering the PWM multiplier, adjust so it doesn't reboot when fully loading the tip, this will reduce the noise.
I can't tell the optimal PID settings, it's depends heavily on the filtering, the ADC frequency, the calibration... It would be easy if we had only one controller type, but there'ro dozens of variations.