That does look like the fan polarity is reversed. That's the first thing I'd try. Normally, the fan should spin clockwise looking from the top.
The smoke looks odd when you start, then starts looking better as you go faster, that's the same thing I've observed with the fan wired backwards. The fan gets a full 5V when it's moving, and a reduced power when stopped, so you should get a more robust puff at slow speed.
FWIW, I normally connect the motor to a bench supply and verify which should be the positive terminal and then mark it with a red mark. Then when I'm wiring, there's no doubt where to connect the positive lead.