Hello from JustAnswer.
There is a very good chance that this is more than simply due to the tea. It is certainly true that drinking significant amounts of any caffeinated beverage late in the day can cause increased urination during the night. But if you are noticing problems no matter how little or much that you drink, that would typically indicate that there is another issue present.
The most common reason for frequent nighttime urination is benign enlargement of the prostate. The vast majority of men get some degree of symptoms from benign enlargement, although the severity of symptoms can vary widely. The usual approach for such symptoms would first be an exam, and then medicines to help ease the symptoms. The most commonly used medicines are alpha-blockers, such as tamsulosin, although medicines to block the effect of testosterone on the prostate, such as finasteride, are also frequently used. In a man with more severe or persistent symptoms, surgery is also an option.
If you are looking for ways to try to manage this without seeing your doctor, there are some herbal supplements that can be tried. They are not as effective as the prescription medicines, but they can be tried to see if they work for you. The most commonly used herb is saw palmetto, but other herbs include red clover, soy isoflavones, or African tree bark.
If I can provide any additional information, please let me know.