He's probably doing a full MEPS process, which means he takes the ASVAB on the first day, spends the night in a hotel, and takes the physical and swears into the Delayed Entry Program on day two. Recruiters often try to get applicants to go down for the full MEPS program right away rather than just taking the test, because the longer the applicant waits to sign the bigger the chance they will bail or sign up for another service. This was probably his recruiters intentions the whole time. There's some real sneaky recruiters out there. Anyway, keep in mind that if he does swear in tomorrow, he's only promised to make a commitment. He can still change his mind, though the Navy will not like it one bit. You shouldn't worry about him shipping out the next day... those things rarely happen these days. It's possible of course, but I've heard people waiting to ship to Navy boot camp from an average of 3-8 months these days.

That being said, good luck to your son. Especially if he goes into the Nuclear program.. that stuff is the real deal. He may have to be in for 6 years, but afterwards he can expect some serious $$$ if he sticks with it post-Navy.