I have attached the picture you sent of your timer wiring.
It looks like you have an Intermatic P1353 timer, which has three single pole switches. These timers have several different ways they can be setup. Based on your previous comments I have a guess at what may have happened.
It is fairly common to have the P1353 setup to only switch one leg of 240 volt power (which has two hot legs). That means there is 120 volts present (relative to ground/neutral) on one of the two hot wires going to the pump and/or SWG. It is always better to switch both legs of 240 volt power, so there is no voltage present at the device when it is off. However, this is not always possible with a P1353 (depending on mode and other devices connected).
If you had it setup that way, only one leg switched, their comment/complaint sort of half makes sense. However, this is more of a long term safety issue than a day to day risk. There has to be something else fairly serious wrong before that can make any difference at all. When only one leg of a 240 supply is live, the only way for current to flow is for there to be a short between the other leg and ground/neutral. And if that were the case the circuit breaker would blow any time the device was fully turned on
Assuming I am not way off, I did some guessing here, then their claim that this could have damaged the SWG is ridiculous. I figure they are grasping at straws. Something is going wrong that they don't understand, and they are following up on something trivial that couldn't actually be the cause because they don't have anything else to follow up on. Having done a lot of tech support I sympathize with them. Figuring out tricky problems remotely is not always at all easy. Often, following up on something that is only kind of strange, rather than actually wrong, reveals the information you need to solve the problem.
Anyway, the short version of this long story is that the voltage/wiring issue referred to almost certainly has nothing to do with the rest of what is going on. There is a minor safety issue here, and their new wiring proposal is better, but I can't see any way it could have anything to do with any of your other issues. All assuming I haven't completely mis-interpreted some slightly cryptic comments you made/passed on.