Just to clarify, most of the movement of your fingers is controlled not by muscles in the fingers themselves, but by tendons, which in turn are controlled by muscles in the palm, the back of the hand, the wrist, and the forearm, going all the way up to the elbow. The muscles in your upper arm don't control the fingers directly, but come into play when you move your hand back and forth on the keyboard.
That's why when you've been practicing a lot your wrist and forearm feel tighter. "Finger strength" is a misnomer.