"Dont want to lie and say i cant get out"
Yes, I understand your situation and I'd like to give you the best advice I can. It might not be the most popular and it is my own opinion, but I believe it is accurate and thorough. I was in the Navy, in the nuclear power program. I also was a field recruiter and a Nuclear Field recruiter.
First, it might seem that people are encouraging you to become independent. I don't believe they fully comprehend how tight-knit Asian families are. It's just something you grow up with. Even if the family doesn't outwardly portray itself as Chinese or Japanese or Vietnamese in order to better integrate into American society, family values are something that are always there. Yes, on one level, your parents will be proud of you. However, I don't know your family in order to say for sure. My parents seemed supportive although they had no say in my decision (I was 24 and was living on my own), but I later have come to realize that my mother was very upset and my decision affected her greatly. She had hopes that I would become a doctor like my grandfather. Both my parents are college-educated and assumed that I would complete my degree before entering into a profession. If your parents don't have those kind of goals, it may not affect them as much as it affected mine.
Right now, you basically have a gentleman's agreement with the Navy. They have agreed that if you enlist at the end of your DEP period, you will get the training you were promised when you agreed to enter DEP. You have given your word, much as an athlete who has signed a letter of intent to a certain college. Your time in DEP does not count toward your time in service.
Having said that, you are not an active duty member of the armed forces until you raise your hand and take the oath immediately before shipping off to boot camp. Until then, you are not subject to the military code of justice. The military will not send anyone to get you. There is no effect on your civil record. You will not be excluded from any government grants or scholarships or other benefits. If you really want the official written policy, I am sure I can find it on the Internet, but forgive me if I don't want to do that right now. (I have homework I should be doing.)
Right now you don't have to do anything. If you don't show up, there is nothing your recruiter can do. However, I don't believe that is the best thing. Sure, it is part of your recruiter's job to deal with these things, but at the same time, I'm sure you don't like it when unexpected things happen. Just as you agreed that you were going to join the Navy on active duty on a certain date, your recruiter and his supervisor also told the Navy that they would provide a trainee both to the Navy and the nuclear training pipeline. I believe it is common courtesy to let your recruiter know of your situation as soon as possible so that he or she can fulfill his or her word to the Navy that they would have a recruit ready to go on that date. Well, you get the idea even if what I've said in this paragraph isn't strictly accurate.
My impression is that even if your parents have not brought up the subject, that doesn't mean they have just accepted the fact. Perhaps you can put it off until the time comes closer for you to graduate, but surely do not wait until the last minute and assume that your parents have accepted your decision.