Pot odds...the pot was what about 30c on the flop?
You'll hit a 4th heart on the turn about 1 in 5 tries (4 to 1 odds) ...so you want to call about that much to hit in general or you are losing money over time.
Not only don't you call 80c into a $1.10 pot (terrible pot odds - do this every time and 4 times outta 5 you're losing 80c), but you minraise...so now you're puting $1.60 into a $3.50 pot...and implied odds (the chance that you'll get a good bit more money on later streets from your opponent) are pretty crappy for flushes.
In this case it looks like the guy had a lower flush or a nice set to pay off with so it probably worked out...but most people would either bet the flop or fold to the overbet.

Say you bet the flop - 20c or so - then he minraises - you'd have to call 20 more cents into a 90c pot - good odds to chase a flush (better than 1/4 the pot to call).