The tea tree oil is a kind of natural sanitizer which would apply to treat many diseases especially the trauma, e.g. cut wound, bruise, insect bite wound, acne, burn, urinary tract infection etc. Recently, it has been widely applied to cosmetics, toilet articles and veterinarian articles. Its fragrance would use to refresh someone's brain. However, the main function of this oil is used to treat trauma, the eyes are so subtle and sensitive. The oil is sticky, it will bring some trouble for your vision, makes you hard to open your eyes, if the oil drops into your eyes. As for the eyes, it will reject any foreign bodies which get into it, so I think this is not a good idea to use tea tree oil for the watery eyes. You would better go to doctor, or use eye drops at first, if this symptom is induced by infection. If it is only because of eyes fatigue, you must relax your eyes for a while. That is simple to do, but please do not use the ways of random to treat your exquisite organ, the eyes.
Generally speaking, watery eyes means too many tears in eyes. It also reflects that the tear film in your eyes has some problems. However, tea tree oil is one of aromatherapy oils, which works for wrinkles and puffiness. You cannot drop them into eyes, or eye infection may occur. In daily life, you can apply some tea tree oil on the skin of eyes to prevent wrinkles and reduce puffiness and dark circles. For watery eyes, you had better visit a doctor and determine the root reason for your condition. And no any self-care without the instruction of your doctor, or further eye infection and eye disorders may follow you.