From the phrasing of the question I'm assuming that you used the King's Court to play the Hireling three times in a previous round.
The King's Court and Hireling do indeed count towards the number of Action cards in play in the current round, but that's just two Action cards in play, not three or four. There's an important difference between Action cards in play and the number of Actions played.
The KC and Hireling count as two Action cards in play in both the round in which they were played and all subsequent rounds. Well, just so long as you don't use Bonfire on them!
The KC and Hireling made a total of four Actions played in the round in which they were played, but zero in all subsequent rounds.
Quite a few cards care about the number of cards in play, but I think Conspirator is the only card for which the number of Actions played in the round is significant.