I have tea dyed hundreds of things successfully and here are some tips. Tea can dye evenly if you use the following hints...
Make sure the garment is THOUROUGHLY soaked through with water first, as warm as the fabric can stand without shrinking (this opens the pores of the fibers and allows them to take more dye). When the garment is thoroughly soaked wring out as much water as you can.
Have your tea dye ready on a stovetop in a large pot (borrow a pot if you need to), that you have put in many tea bags in and have let boil for 15 minutes, and have removed the tea bags from after squeezing all the liquid out.
Leave the stove on "simmer" and put in the garment, pushing it down to make sure it is ALL covered with the tea.
Stand at the pot and stir the garment while it "simmers" for 30 minutes, making sure the garment is under the liquid the whole time.
Remove the garment at the sink and gently squeeze the excess tea out.
Dry in the dryer on as hot as the garment can stand without shrinking, (this will set the dye/tea).