Like Rewben2 said, I get tense when I'm nervous (usually because I'm about to set a really good score). It limits my ability to play as I have to squeeze the mouse hard and I know it's not good for my hands because it tires me out a lot quicker. It's a lose-lose for me, basically. I also find my left hand gets tense though when I need to make extremely accurate taps, such as doing repetitive long jumps around the map. I'm not sure if that actually helps with the timing though, it's sort of automatic.
Anything that can make you more relaxed while you play would help.