You need click to move on.
You need interact with target keybound.

Go with two steps.
Either two presses or press and release will work.

Verify the toons will run towards an npc.
And that the second step will break the movement.

I know there's an option to auto switch from melee to ranged attacks for some classes.
Not sure if that causes an issue.
You'd want Interact with a hostile target to cause your team to run and melee them.

I know my feral druids will run at something to melee it, even when casting wrath in caster form.
Unless I hit my Melee IWT toggle key, to disable IWT.
I don't have a mapped key on this team, for IWT + Break movement, but down arrow breaks the movement.