This happens time to time with lighter braid and especially on certain brands that may not use as many strands. Spiderwire is very good, I put 15lb test on my son's spinning reel and have no issues with line twist and no issues with it digging into itself (although come the colder month's it's still a possibility), but I like the Daiwa J-Braid even better, it seems to frey a little bit less. With some other brands of braid especially with lighter line, you may have issues.
I also backed it with a few solid wraps of monofiliment as well. I would say I put just enough on to make sure the spool is solidly covered in every spot, but not much more than that.