Well somewhere you have some common impedance that is allowing the voltage in the aux garage to drop when the load is applied. Motors have a high start-up current which makes them the most common reason.
However, if it really is a 200A capable panel there is no excuse as the tub can't be taking a sizeable chunk of that much. Usually the reason is the supplying cable is not thick enough for the length even if it meets the current carying capacity ('ampicity' I think is the USA expression), but more worryingly it can be down to a bad connection and that presents a fire hazard due to it heating up.
I see you are down as USA location, so maybe one of the American members such as
@Megawatt will be along with a bit more country specific