I had this happen to me on 4 out of 12 arrows that I made. This did not help my confidence, as this was the first 12 Cedar arrows I ever tried to make several years ago.
They were POC woods arrows, and I made sure while constructing them that the grain orientation was perpendicular to the string. Had that covered.
The arrows split exactly like you show above. 3 of the 4, sheared off so quickly that it essentially dry fired my bow 3 times. These failures all occured on the same outing to our shooting club.
What I think happened, is that I used a highly "fumatic" fletching glue in conjuction with glueing the nock. The nock's glue bond to the woods shaft never faultered. It always split right down the middle, but stayed adhered to the shaft. I was dumb-founded at how this shaft could split down the middle like that, with the grain orientation correct in comparison with the string... Amazing! And SCARY!
The only determination I could make, was that the glue reacted negatively with the plastic nock, essentially breaking it down or weakening it. A change of glue (Kimsha Hot Melt) and I've never had it happen since.