I think most people would probably agree that Tidal Wave counts as running water, and there's no definition of running water in D&D 5e to prove them wrong. More importantly, your DM agreed, and its their opinion that matters. So Tidal Wave does count as running water. Unfortunately, for the most part it doesn't actually matter.
Tidal Wave has a duration of instantaneous, and ends with this sentence:
The water then spreads out across the ground in all directions, extinguishing unprotected flames in its area and within 30 feet of it, and then it vanishes.
Importantly, the "and then it vanishes" was not present in the original Elemental Evil Player's Companion, which might be why you weren't sure how long the water lasts.
So the vampire will only be in running water at the moment the Tidal Wave spell happens. Therefore, there's no way for Tidal Wave to trigger this:
The vampire takes 20 acid damage if it ends its turn in running water.
Similarly, there's no way for Tidal Wave to trigger this:
The vampire regains 20 hit points at the start of its turn if it has at least 1 hit point and isn't in sunlight or running water.
However, there is some good news:
When it drops to 0 hit points outside its resting place, the vampire transforms into a cloud of mist (as in the Shapechanger trait) instead of falling unconscious, provided that it isn't in sunlight or running water. If it can't transform, it is destroyed.
So if you reduce a vampire to 0 using the Tidal Wave spell, it will probably be destroyed instead of escaping to its coffin. Obviously, this will require some pretty serious metagaming (or just getting really lucky).