Why will someone say it happened instantaneously instead of just saying it happened instantly?

Instantaneously generall implies a relationship. For instance, “The explosion happened instantaneously to the take-off of the rocket.” The explosion and the rocket are related. Instantly means “at once” and does not necessarily imply a relationship. “The coffee began percolating instantly.” is only about the coffee itself. People misuse these and other words all the time, but this is how they should be properly used.

depends on the time of day for me

They want to sound smart. That’s really what I think.

I say “immediately” myself