How long did it take for the light from those atomic explosions to reach these presupposed aliens? The maximum distance would be about 65 light years, wouldn't it? Yet you say that UFO sightings are date co-incident with our dropping the first atomic bombs on Japan. So your theory means that the "advanced civilization" must either have already been here, or relatively close by. But why would these supposed aliens have already been here, before the atomic bombs were dropped? What, they were listening to AM radio broadcasts? If they were already present when the bombs were dropped then those explosions have nothing to do with them supposedly being here.
Cordially,
ETs could have had sensors or local outposts in this sector for thousands of years prior to WWII, for any number of reasons. Those sensors would have picked up and relayed the signature of atomic detonations, which would have brought on an investigative mission.
That's one theory. I can think of others.
There's every chance that the Sol system is already a territory of some political entity, such as a confederation, empire, or such. If so, there would be remote monitoring, at the very least. Face to face contact would likely be discouraged (if not banned) because of our relative primitive state of evolution.