User blog comment:B214/Question and Answers 6/@comment-82.2.190.195-20161102162156/@comment-1359322-20161102173614

That's unique to Issei's own Evil Pieces in short his Pawn Pieces. The King just imbue their Demonic Powers to activate the Evil Pieces. After that process is done, the remaining things like power-up etc is related to the servant itself not the King.

Sometimes the servant can be stronger than the master sometimes they don't. But the King isn't really linked to the servants through the Evil Pieces that's why Stray Devils exist. That's also why the King don't get the Servant's powers/abilities. You don't see Rias having the ability to use time stop or healing like Asia's.