Generally the set pressure with a BPR is the cracking pressure.
Pressure experienced in the system should not much exceed 45 psi. JLSeagull is correct that they should act with proportional only control but the proportional band should start at 45 psi. Typically the proportional band is about 10% of the range, so if these are adjustable to 60, the PB would be about 6, so cracking at 45, full open by 51 on the first one. (actual numbers may vary, but you get the idea)
In a first-ever event: I apologize for being blunt but I think insult 2 injury is wrong. These are not like parallel resistors,if you want an electrical analogy, but more like parallel zener diodes. The breakdown voltage is analogous to the setpressure, and there should be no flow until the pressure reaches the magic number. UNLESS THE VALVES ARE STUCK OPEN.
This is weird, and I think you will find that they are using a remote sensing line on the high-pressure side of a partially-closed balancing valve or some such strange piping effect. Verify that the sensing point is actually at the point of interest.
Without knowing the type of valve, there may be one other possibility: If it's a balanced valve installed with the flow direction reversed, the balancing would be defeated and the hydrostatic forces can be forcing the plug open when it should be closed. Check flow arrows on the valve bodies or tags.