To avoid smudges on your T-shirt, always apply 1 to 2 coats of textile primer, depending on the flexibility and thickness of the textile. The thinner or softer the garment, the more coats you'll need. If it's thick, a single coat may be enough. And if in doubt, better too much than too little.
Make sure your brush isn't too full of paint, and never put the first drop of paint in the stencil. You can, for example, spread the paint on your palette or on the tape around the stencil.