Pump running, almost always.
The whole point is immediate dilution. If you add chemicals with the water still, especially heavier stuff like liquid chlorine, acid, or dissolved calcium, it can sit in one area and create a super concentrated “hot spot.” That’s how liners fade and plaster gets etched.
I usually let the pump run at least 10–15 minutes before adding anything so there’s good circulation, then add slowly in front of a return so it disperses fast. After that, I keep it running at least 20–30 minutes, longer if it’s a larger adjustment.
Only exception is something like stabilizer in a sock method, where it dissolves slowly anyway, but even then the pump should be running.
So yeah, pump on isn’t just preference, it’s safer and more consistent.