Is one considered in the Air-Force once signing the DEP contract?

Hey im a DEPper too in the Navy, Cheif told me that for the airforce there are no job opennings there, so they supposedly make you sign a blank piece of paper. Anyways I considered myself personally part of the navy as a DEPper, but other people like in school dont consider me one yet until I p bootcamp. Once I graduate Naval bootcamp, i guess people start "seeing" me as a US sailor.