Yes, normal = all four pumps running. In a PWR, your analyzed safety margins generally say "percent total flow through the core must be equal to or greater than total percent power."
So to get full output from the plant (100% power) you need 100% flow - all four running. One pump trips, and total flow goes to ~82% (hydraulics, pump heads, etc. Not a simple 75%.)
But power hasn't changed yet. 100% > 82%, automatic trips kick in and shut the plant down. You haven't damaged anything because the designed safety margins and trip responses take the transient into effect.
Can you run on three pumps? Sure, just not at full rated output. And since your job is to produce as much electricity as you can, the typical civilian plant is binary - either shut down or 100%.