Q: When the Taskmaster gives me a card, does it temporarily become my turn?

…If the card I got is a Draw or Play increase, do I get to enact the usual consequences: Draw the difference or play the extra cards in addition to the card I was just given?

A: No, it is still the Taskmaster’s turn even though they’ve given out cards for others to put into play. When people take turns playing the cards given to them by the Taskmaster. It’s like the Taskmaster is in charge, and has told you all, their minions, to take these cards, and put into play (put them into play as you would as a tur, and that’s it. It’s still the Taskmaster’s turn. What this means for each type of card is this:

New Rules and Goals go into play in the middle of the table just as though the Taskmaster themselves had played them. If there is Draw or Play change it’s going to affect their Draw, and their number of Plays remaining. If it’s a Limit, it’s all the rest of you who are going to have to comply immediately. The active player (the Taskmaster) will not have to discard down to Limits until their turn is over.

If it’s a Keeper, the person given the card to play gets to put it in play in front of themselves.

If it’s an Action, the person given the card gets to do the thing. For example, if it’s Jackpot, they get to draw 3 cards. If it’s Steal a Keeper, they get to steal someone else’s Keeper for themselves. If it was Draw 3, Play 2 of them, they get to set their hand aside, draw 3 cards, play 2 of them, and throw the remaining card in the discard.
* What about Take Another Turn?

Surprises should be played for their in-turn function.