I'm not sure that it is possible in skirmish maps to assign units to a "discovering" player. Those triggers in the singleplayer maps don't assign units to the "discovering" player, as there only is one player who could discover them. The singleplayer triggers are along the lines of "the player has put one of their units in this trigger area, so transfer these extra units to the player." The player's specific house is what's cited in the triggers.
Your best workaround might be to somehow put the units in an area where only a specific player can access them, then you can invoke the "Player @ X" logic. For instance, you could maybe have your units in some sort of terrain-blocked area where the only way in is through an indestructible and uncapturable neutral building blocking the entrance. You could then set up a trigger where this building sells itself when a player from a specific starting location draws near, and then units are transferred to that player... but it's a bit of a faffy workaround.