The spiral shape was present when they were created and likely part of the ritual or simply a ceremonial formation; so that's not their own in any way, just a repetition of something done by The Children. There's obviously some symbolism there, but if it's explained or not...:shrug:
As for turning on The Children, we don't really know if that happened immediately or not. From the partial history we know that they called a truce, man would rule the "open lands" (plains, mountains, swamps) and the Children would take refuge in the forests. Then it was thousands of years before the Others invaded and the pact was tested. So I'm not sure whether or not the Walkers turned on them right off the bat, were defeated by man alone whom then fought the Children to a standstill, they just wandered off after being created to gather strength, or what. It could be that after the Children and the First Men teamed up they were then considered a part of the single enemy that the WW were tasked with destroying. Hopefully we get some answers -- just leaving it at "they were created by the Children to fight the First Men, and now they're evil" would be incredibly shitty.