Your pattern does not given specific increase guidelines. It says to do so as needed. This will likely be true for any pattern like this, as you cannot be certain of consisitent fabric thickness and thereby consisitent size/growth.
After doing your first round, then increaseing in every loop for the second round, I would suggest you proceed as follows...
Lay the piece down/flat. Wrap the next bit of fabric (several inches) along the edge of your circle and pin it in place. Then work along this section (attach via crochet/yarn) making increases as needed to hold the fabric in place. When you get to your last pin, repeat.
In theory, the increase ratio should work out something like this.