How many local co-op players does Mario Kart 8 support

The controller used by the first player is the controller that was used to pass the title screen, before the menu where you can select "Single Player", "Multiplayer", etc. You can pass this title screen with any kind of supported controller.

If the wrong controller has been used, you can back out to the title screen with the B button and start again with the correct controller without needing to reset the game entirely.

I just tested this as well (with a standard bike; you appear to have tested with other karts enough) by doing donuts in Dry Dry Desert. I do indeed see the same automatic boosting behavior on sharp turns.

This appears to be a subtle feature of the game that isn't obvious or well documented.

I can't say "why" this exists without consulting the developers, but if I had to guess I would say the automatic turn boost is there to assist with turning in situations where you weren't able to pull off a drift - drifting always goes to the outside (even with sports bikes, during the early part of the drift), which means in some situations you might not want to risk drifting. In those cases, this turn boost could kick in.

It's pretty hard to do on purpose, but when it happens it can only help - as far as I can tell, other than giving you a speed boost, this automatic turn boost does not affect how you turn.