Rarely. A few sensitive to either the caffeine or some other alkaloids in coffee preparations can develop lid twitching. Not too common so starbuck's can continue to feel safe.
Can contribute.. Twitching eyelids are extremely common. Can last for weeks and suddenly disappear as abruptly as it started. Caffeine and stress can worsen. So can low magnesium. Don't be concerned unless persists more than a month or so or if it is a forceful lid closure that prevents opening the eye.
Sometimes. A number of things may cause the eyelids to twitch. These include caffeine, fatigue and stress. If this persists you should see an eye doctor for evaluation.