Not sure, honestly.

For this to work you need the order to be the same on all screens. If the healer is always targeting the same toon with their heals, irregardless of the box you are clicking on, then I would assume it is something to do with Healbot.

If the mouse is broadcast (via repeater) to the healer's window, and you can move it from one box to another (ie, change targets, even if Healbot is not recognizing the target box has changed) then the Repeater region is probably not the issue.

I'm not terribly familiar with Healbot, but that is where the issue will be. See if, from the Healer's screen you can click target your heals on each of your party members. Once you can heal whoever you want to, from the Healer's window, the issue should be resolved.