Tea contains hundreds of active ingredients, among which you find theine, antioxidants, tannins, vitamins and microelements. Therefore, yes you will find theine (which is the same as caffeine) in tea.
However, the amount of theine in the tea depends on which kind you're talking about. Green tea like Sencha, or white tea (Yin Zhen, Pai Mu Tan) contains a small amount of theine. Black teas usually have a higher content.
Also, it depends on its quality, i don't want to spit on them but there really is a difference between supermarket teabags and loose leaves teas from tea stores (which can also be sold in individual muslin bags). The supermarket varieties are almost powdered teas with lots of tannins, responsible for the bitter taste. On a side note, muslin is the best stuff for a good brew.
So try getting some loose leaf green tea (white is more expensive), you can also try rooibos which doesn't contain any theine, or detheined tea.
Technically theine only develops in the first minutes of brewing, tannins develop as long as you keep the teabag in the cup, and they attack theine. So if you let your tea brew for a long time, you should get a tea without much theine. The risk is the tannins' bitter taste.
I read you can also run your tea bag under tap water before brewing it, but that i haven't tested.
Anyway, if you use the tea just on your face, just brew it as usual. If you want to drink a part of it, well that's up to you, i personally would still brew it the same way. But i thought caffeine had positive effects on your skin (blood circulation ?), so i don't really bother with whether or not my tea contains theine
