My understanding is that this only happens on ships that call at a US port after having called at a foreign port. So this would only have to happen on the Magic, not the Wonder. The Wonder calls only at the Bahamas, so you'd only have to pass through US Immigration when you return to Port Canaveral. The Magic stops at St. Maarten, Netherlands Antilles, and then St. Thomas, USVI, so the immigration check happens on Wednesday morning in St. Thomas.
Bad news that they've re-instated this. I'd be interested to hear if other cruise lines are still doing this. Disney swears up and down that it is the US Immigration and Naturalization Service that requires it. If that's true, I would suspect other cruise lines would have to do it if they follow a similar itinerary. I've heard anecdotal evidence that some cruise lines don't have to do it, but I've never been made clear what the itineraries were in cases where it didn't happen. For example, if you sail from Miami to San Juan, to St. Thomas, you've called only at US ports. If the next call was to the Bahamas before going back to Florida, I can see that you wouldn't have to go through immigration when calling at St. Thomas. That's assuming I understand the guidelines for this immigration check....