I'm pretty sure that invisible characters are supposed to get revealed breaking the status, but in my case the character stays invisible even after using damaging abilities/attacking. I'm guessing that there is a script somewhere that dictates a status to be removed when dealing damage out of cloak, but I was unable to find the script for it.
Invisibility removal is handled by Statuses.gameScript. You can recreate the same sort of behavior in your mod of course, but personally I prefer applying the regular INVISIBLE and a hidden additional status to go along with it. A status is hidden when it has no icon set.
As long as you're fine with using the same visual effect and StackId/Display name as INVISIBLE, that solution ends up being a bit easier / more compatible in the long run, as Larian checks for the INVISIBLE specifically in other scripts for things like combat comments and seeing if a player is hiding.
How are you applying your damage on move status? Damage on move statuses have extra parameters that determine the distance required before damage procs, which (from what I've gathered), can only be applied by stats like so:
That last number is the distance required before damage happens.