>>I guess that it must fill quickly

Yes. However, the full stroke of the cam isn't normally used.

As the fuel is delivered by the spring, the piston only moves along the bore of the pump corresponding to the amount of fuel delivered. As the piston progresses, the spring force pushing it drops as the spring extends. This means that the over-pressure that the pump produces compared with the relief valve opening pressure drops, and the fuel flow rate slows. If the cycle happened slowly enough, the piston would stop as the relief valve shuts, trapping fuel at pressure in the system.

The worst case of pressure fluctuation happens at low engine speeds, when the piston has the longest time to deliver fuel - at higher engine speeds, the fuel pump's piston will barely move, and the pushrod will only touch the IP cam for a very small angle of IP rotation.

The full stroke of the cam is only used when there is no resistance to pump against - say if there's a lot of air in the system, or if the relief valve has failed in the open position. The large spurts of fuel one sees when cranking the engine with a pipe off are much larger volumes of fuel than the lift pump normally delivers each cycle.