They don't have to back the train from EMY into the yard like the would from OKJ, just pull forward. The two stations are just a couple of miles away from each other with the yard in between.
Amtrak has a coach yard between OKJ and EMY, they don't have the facilities to service a long distance train at SJC.
They used to run into OKJ, but it just took extra time and trouble to get the train to and from the yard involving reverse moves. Wasn't worth the trouble and expense just to save a couple of miles so they changed the terminal to Emeryville.
OKJ of course is still there. It replaced the old SP station at 16th and Wood which was closed after the Loma Prieta quake (after having used temporary quarters at 16th and Wood for awhile). Now it not only doesn't have train service, but no tracks, the tracks having been moved for the construction of the new 880 replacing the collapsed Cypress Viaduct. Now the 880 freeway is between the 16th and Wood station (still standing) and the tracks. The 16th and Wood station was north of the yard, and the street running, too, so backing the wasn't an issue when they used the old SP station. There was no Emeryville station back then, either. Arguably, the EMY and OKJ station pair together are the replacement for the old Oakland SP station (Amtrak station code OAK).
BTW, the 16th & Wood SP station was and is in a spectacularly bad area of West Oakland. Both EMY and OKJ are in better locations and they are both better served by public transit than 16th & Wood was.
EMY is more convienent to the Bay Bridge, too. Shorter connection times for northbound and eastbound trains. Passengers coming or going to the south on the Coast Starlight San Francisco connection buses do go to OKJ. Going north on the Starlight, the San Francisco buses connect at Emeryville.
All in all Emeryville makes all kind of sense, with very little justifcation for terminating at OKJ.