My thumbs and fingers twitch when they're bent in certain positions. Is this a cause for worry? They don't twitch any other time.

Spasms. This sounds like muscle spasms. Common causes are a relative dehydration or a vitamin deficiency. Consider drinking more water and adding a multivitamin daily. If it does not resolve then talk to your doctor about it.
Doubtful, but... Positional muscle twitching can occur; is this a new finding? If so, you should be seen by your local PCP for further evaluation.
Twitches. If you forcefully bend your fingers in certain ways it can affect your nerves and blood vessels and that can cause twitching. Please see your doctor also to get evaluated for any other isssues.