As you see, Synchronoise is learnt by breeding, and that Eevee learns it by that method.
As Eevee evolves into Umbreon, Umbreon has that move as well, despite being as useful as Splash in the context.
This is seen in many moves. Any moves Eevee learns, the Eeveelutions invariably learn. This is how they're coded, and makes sense in general. Sometimes, due to the generalized methods, you get useless combinations like the one you mentioned. There's no point for that, just that deletion of moves from a moveset upon evolution is somewhat absurd, and is rarely if ever, seen. If a Pokemon knows just one move, and evolves, but the evolution doesn't learn that, then there's going to be trouble. Imagine your Eevee knowing Tackle, and just before it evolves into Umbreon, you delete every move apart from Tackle, which, say, Umbreon can't learn (for example). Will you get an Umbreon without moves? Same principle here.