When you say black tea, do you mean just teabag and hot water?
It's possible that that your toothpaste contains a sweetener. Many non-sugar sweeteners can still raise BG in some but not all even if they have no calories.
The same applies to mouthwash.
But your BG can rise even if you don't eat or drink anything, because your liver tries its best to keep your BG inside the range your body is used to (which may be higher than you would like) by either dumping stored glucose into the blood stream or by making fresh glucose. The liver is the main 'chemical factory' for the body. Read up on Dawn Phenomenon.
It needs to be able to do this since otherwise humans would be unable to fast, because certain brain functions require glucose for fuel and can't work on just ketones alone, unlike the rest of the brain and all or the rest of the body.