Exploding kittens - playing cards between attacks
The other cards do not end the turn so they have no effect on the number of turns played.


Player A has 1 turn to play.
Player A plays Attack. 


This ends the turn of player A
And it forces player B to take 2 turns.

Player B has 2 turns to complete.
Player B plays some other cards (Favour, See the Future or whatever). 


This has no effect on the turn because the turn only ends with a draw.

Player B has still 2 turns to complete.
Player B plays Attack 


This ends the (first) turn of player B.
It forces player C to take 2 turns.
Because player B has one turn left, this turn moves to player C.

Player C has 2 + 1 = 3 turns to complete.


See also the rules.