My peg tube leaked as you described for a week couple weeks, as I recall. I think the brown is liquid from the stomach. The skin never really gets tight around the tube, so some leakage is normal. I used square pads with slits for a while just to absorb anything.

My tube site also became infected, but that was much different. Bright red skin, puss, very painful. See a doctor if that happens. That had to be treated with antibiotics.