Maintenance Controller reported difficulties during ground troubleshooting of an Engine Bleed Air issue. It was later reported that the Captain who accepted the aircraft elected to divert instead of continuing the flight.

Narrative

I received an ARINC call from the inbound Flight Crew ZZZ-ZZZ1 reporting right duct pressure surging/fluctuating with cabin rate of climb fluctuating 300 ft. +/- with pressurization normal. ELB LP XXXXXXX and XXXXXXY reported the same. I had the on call Maintenance Technician perform RT Pack Temp controller bite per manual XX-XX task XXX with no existing faults found. Technician ran both packs with APU bleed air and no surging or fluctuating pack noted. I then spoke directly with the outbound Captain requesting for the crew to perform an engine run at the gate to check if the duct pressure fluctuation was engine related. Outbound Captain said that he would take the aircraft and check for any fluctuation during taxi out that he would return to the gate. Captain also indicated that if fluctuation happened in flight that he would divert to ZZZ1. I agreed to the actions of the Captain because there was no history of pressurization; RT Pack or engine bleed actions by the Captain. During taxi out the crew called about a zone temp light discrepancy. During that call I asked the Captain reported no issues with packs or engines. I was made aware of the diversion by Maintenance Manager via email. I provided link with the same statement I am providing in this report. ZZZ1 replaced the right PRSOV to fix the problem. I should have taken the aircraft out of service and send a work order from ZZZ1 to perform a high power engine run.