Yep, I agree.
Placing Overwatch in this situation simulates you pointing the gun at the opponent, whiile they still have theirs holstered, possibly even with a slight grin as you know you have the advantage.
Tactically it causes the opponent to freeze to the spot, momentarily, while you cover them with your gun.
You'd use it, rather than attacking directly, if there were multiple opponents possibly that you wanted to try and cover, or that you had another character that you wanted to activate first and didn't want to lose the opportunity to attack Eva.
If Eva doesn't move or act that round, then the moment of covering is over (i.e. the turn ends) and next round you choose to either continue covering her (set overwatch again), or open fire on her (act normally).
If you don't set overwatch AND lose initiative and Eva slips away, that just represents you momentarily taking your eye of her; perhaps an explosion from a grenade in another area of the map distracts you.
....We've all seen this in the movies, how more realistic can you get?!