In reality, I think this less well known excerpt[1] from the deservedly short lived "Nightly Show" better captures how humanity would react to aliens. In the excerpt Bill Nye is trying to hype people up for the discovery of water on Mars - the other panelists though just don't care. The audience and the host don't really seem to care either.
This is basically how I think people will react to aliens. It won't cause a panic, some people will be somewhat interested. Oh, aliens exist and sometimes fly around in our atmosphere? Okay, cool. I expect most people will say and believe that they "always knew" UFOs were real.
As near as I can tell it seems like the interested US government programs believe there are advanced flying objects of unknown origin operating in our atmosphere and they publicly acknowledge this. This is also not an enormous topic of conversation.
Two days later, I found out that an elder relative passed, having had suffered from a heart attack. He died over a 24 hour period and was with his family. The thing is, I had no prior knowledge of his condition or even any contact with him at all in a long time.
I've speculated about the cause and implications. Perhaps I hallucinated. Maybe aliens took my relative. Or was it "God"? Is there even a distinction?
Horatio:
O day and night, but this is wondrous strange!
Hamlet:
And therefore as a stranger give it welcome. There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.
There could be another explanation, that the event you describe a result of confabulation; essentially an error in memory where you mind fills in the gaps. The problem is that the more you explore such a memory the more real it becomes as you mind interpolates it.
Sure, people do retroactively interpolate foggy/inaccurate memories to fit missing puzzle pieces, but this event was incredibly distinct.