There are a number of methods for reducing a square or triangular cane. One is to use a brayer or rolling pin on each side successively - roll a bit, then rotate and roll on the next side, and so on until you reach the size you want. Another is to hold onto one end of the cane and tug gently, sliding your fingers along the cane's length with the other hand. With this method also, you should alternate sides and alternate the end you're tugging. Turn the cane over frequently so you are reducing all its sides evenly, and make sure you're not crushing the corners.
All cane reduction needs to be done carefully and gradually.
Trying to reduce the cane too fast will distort the design. All reduced canes end up with strange-looking ends, with some parts of the design extruded. It's an unavoidable consequence of reducing the cane, and completely normal. Some clayworkers press a small disk onto each end of the cane before they start reducing. You can use the ends as scrap clay, or marble them together to make beads that coordinate with your cane's colors.