Aside from anything the PSU or tester documentation might tell you...
First check any AC mains voltage select switches for proper setting.
If PSU tester was connected while PSU was also connected to ANYTHING in the PC, then disconnect those connections and retry the PSU tester.
Then, assuming the PSU tester test was performed with the PSU NOT connected to ANYTHING in the PC...
Then, I'd say highly likely.
You should also check for any damaged wires and connectors, and fans that aren't running. It could be a wiring problem, or the PSU fan might not be running at right speed(s), or fan sensor or sensor wiring or fan power wiring damaged, or internal fuse blown in PSU due to prior activity..
If possible, I'd go for something other than Bestec 250W PSU. One, it's very low power and won't handle much beyond a minimum configuration. Two, there are better quality PSUs available for reasonable cost.
I found that an US$80 (retail at the time) Ultra V-series 500W ATX series PSU was an exact physical replacement, screw-for-screw, fan and AC powerplug location, etc. for a Bestec 300W PSU in an emachines systems. I also checked to make sure the cables came out of the PSU case in a location that wouldn't be a problem in the emachines computer case.
I got it on sale with rebate for US$20.
Normally, I consider the Ultra PSU an "OK" safe and capable PSU...not great...but OK, and at the price it was defiinitely right for that economy machine. You may find a similar deal. With more PSUs to choose from, you may find something closer to your location.
You'll find recommendations about PSUs all over the net, including these HWA fora.
It does not hurt to get an somewhat overpowered PSU for a given system, as long as the specs are met and it meets your requirements for noise..
Edit to add:
Sometimes, a PSU may not quite fit properly in a given case. For example, the above uLTRA PSU didn't easily fit in a Compaq case, worked ok in an HP case, and didn't fit at all (without modifying) in some off-brand build-your-own case I can't remember. So it does pay to try to figure out as much as possible ahead of time. Going to manufacturer websites can sometimes help with dimensions and details on cable placement, screw locations, etc.