50/50 liability

I was involved in a small fender bender in Texas. I did not submit a claim with my insurance because my car had minor damage. The other person had State Farm and they determined 50/50 liability. I received a letter they would pay for 0% of my damages. I spoke to the claims adjuster and they said they would pay for their persons damages. My question is - will they contact my insurance and will my insurance have to pay for the other persons damages?