If "he has a meltdown" that means he had an extremely emotional moment in public. Saying "he had a full-on meltdown" means that he TOTALLY had an extremely emotional moment in public. 100% emotional. He didn't hide it even a little bit. He cried and wept like a baby in the middle of the shopping mall and screamed when somebody tried to pick him up. It is (usually) a response (crying and panicking) because something happened that the person didn't like. The phrase "meltdown" also implies that it was very bad, but still the person over-reacted

I wonder how many people had a full-on meltdown after losing their jobs and their homes during the most recent housing crisis.

You can have a full-on meltdown. "He had a full-on meltdown". Anger is one emotion, it means to "lose it" over something.