A relief valve set for 1250 psi on a system with a positive displacement pump (2500 rpm) sees pressure spikes of 1275 psi every 1.5 seconds.  However, the RV does not lift.
A Direct Acting Relief Valve will respond faster that a Pilot Operted type but both have to move a mechanical part that is spring loaded and that requires time. A Pilot operated Relief valve can have as much as twice the pressure setting override each time it is forced to open.
You must be reading the 1,275 PSI peaks with a digital gauge so you can see what the pressure spike is if you block pump outlet suddenly.
I always use a small bladder or diaphragm type accumulator as a pulsation dampener and locate it as close as possible to the pump discharge port. Set the pre-charge pressure at or slightly under the relief valve setting and there will be very little pressure spikes in the line to the circuit.

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