Great question. It's actually super common.
Generally yes. If a person gets their PRIVILEGE TO DRIVE suspended in one state, even though they have a drivers license in another state, their home state will honor the suspension.
The only question is "When will the home state find out?"
Although I cannot tell what statute is at issue here, I can say the cause of the suspension does not matter in general. The only relevant fact is that the privilege to drive is suspended.
States can suspended the driving privilege of a person even if they do not have a valid drivers license from that state. It actually happens every day.
And that is why you cannot get a speeding ticket in one state you are visiting, and then just go home and ignore it. In those cases, the visited state would cause a failure to appear suspension, and then give notice of that suspension to the home state's DMV agency.
There may be a way to challenge the home state suspension once it comes. When the suspension notice arrives it should include information on the driver's right to challenge the suspension. But I cannot say if that would help in this situation.