The blow-off actually happens about 90 minutes after the start of Illuminations. Before it can happen, all other fireworks barges need to be cleared off of the water, and any Friendships that will be going off-duty in Crescent Lake around that time need to be parked as well. (Off-hand I don't know if Friendship service continues on Crescent Lake during the entire length of EMH at Epcot)
As some people have said, since the introduction of evening EMH at Epcot, they've added a public announcement with countdown. It's unclear as to whether they do the announcement on non-EMH nights. But a few years ago it was simply just the big fireball with no public warning. (I'm sure there's a LOT of radio communication among the pyro people beforehand)
You can actually stay to see it on non-EMH nights, but like I said, it's 90 minutes after the start of Illuminations. So the park is virtually empty by that point. My suggestion would be to do the security CMs a favor and watch it from the International Gateway area and plan to leave through the International Gateway afterward. It helps them clear the park faster. (Also, resort transportation at the front of the park may have already ended by the time you get out the front entrance)
-Rob