By PSU I assume you mean the R8213 controller and not the transformer in the wall socket that plugs into it.
That assumption is wrong.
Rob does indeed mean the PSU that plugs into the mains wall socket. What he was trying to convey to you in his reply is that the Select controller is compatible with both the 1 amp PSU that ships with the Select as well as the P9300 4 amp PSU that can be purchased as an upgrade.
When the 4 amp upgrade PSU is used, it is the Select that performs the 'short circuit' protection. However, with the default factory supplied 1 amp PSU, it is the PSU itself that is relegated to perform the bulk of the 'short circuit' protection [because the 1 amp PSU cannot supply the 4 amps for which the Select short circuit protection is designed for]. Thus when a 'short circuit' occurs, the output of the 1 amp PSU drops voltage to protect itself. This drop in voltage on the DC power input of the Select means that there is insufficient voltage to maintain the normal operation of the Select and things like fading screen and other observations can happen. The output of the 1 amp PSU varies up and down and trying to stabilise itself for as long as the fault condition exists.
Now it may be that one or other of your locos is causing a 'short circuit' condition. But it is also fairly commonly reported for users to have faulty 1 amp PSU where even normal operating currents [i.e not a short circuit condition] still cause the 1 amp PSU to go into 'protection mode'.
Rob's suggested diagnostic tests that he documented are trying to diagnose whether the fault lies with a loco or the PSU. By measuring the voltage output of the PSU [not the Select controller output] as the track load increases, you can then measure whether the PSU output remains constant at 15 volts DC or exhibits a significant drop in voltage [say less than 10 volts]. If a drop is observed when the track load is very low, then it is more likely that the PSU is faulty.
Note: a low track load, would be when only a single loco is on the track running sedately to moderate.
Note also: that if just the act of placing the loco on the track, even if you are not commanding it to move causes the observed fault condition, then the fault is more likely to lie in the loco.
As you can't access the output of the PSU when it is plugged into the Select, then you would need to make an adaptor cable to give access to the connector pins so that a voltage can be measured. To make such an adaptor you would need a DC coax socket and a DC Coax plug with a 6.3mm outer barrel and a 3.0 or 3.1mm inner pin. You would also need to purchase a Multimeter if you don't currently have one. Given that these components would need to be sourced and an adaptor cable constructed, the easiest option as the set is a new purchase is just to exchange it with the retailer.