Ok, so here's how it supposed to work. If you're coming from initial accession (i.e., USNA, ROTC, etc), and you are not married, then you'll be TAD to API. As such, you'll get the 600 lb allowance. Once you're finished with API you'll be sent PCS to wherever you go from there from either your home of record or Pensacola, whichever you choose. This is because you are going to your initial permanent duty assignment and also because you haven't been permanently assigned anywhere yet. As was stated earlier, if you get hung up down here and it takes longer than 6 months to get through API and you are on TAD orders, go to PSD and make them change it. That way you'll get reimbursed for your time. They have to change it too, since there's some issues about TAD orders longer than 6 months.
If you are married, it's different since you have dependents. Also, if you've already been stationed somewhere (i.e., grad school, or some other place before you came to API, but after you were comissioned, and OHARP, etc, doesn't count) you have to be PCS'd down here. Plus, if you're prior enlisted you should get a PCS move, although sometimes they'll try and get out of paying you the dough. They can't do that since as prior enlisted you've already been moved from your home of record once, and the Navy can't move you from your home of record more than once. That applies to grad school or other stations, since moving there was a PCS due to being longer than 6 months and was either from your home of record or your NROTC unit, USNA, etc.
As for Beans and his PCS orders, API should be listed as an intermediate activity, and if I was a betting man I'd say they list the time as something like
"For Approximately 140 days" or something like that (notice it's a number lower than 180).
Specifically at Beans, first, read your orders. If it says you have an intermediate activity at API and then an ultimate activity at Trawing5 (permanent duty station Fl, Milton), that means you're PCS'ing down here, so bring all your trash. If for some reason the Navy decides to send you to Corpus, guess what, another PCS.
Hope that helps clear up some things.