If it is the former, then the confirmation process continues and if confirmed, Rockefeller takes office. Since it would only be a temporary stint as Acting President that would require him to leave Congress, then both Speaker Albert and PPT Eastland might decline to take office, leaving it to Treasury Secretary Simon (Secretary of State Kissinger being ineligible) to be Acting President.
Can one refuse to take office in such situation? Doesn't a presidential tenure automatically starts when the previous one is out of office? I mean, wasn't Ford already the President since Nixon's resignation took effect, even though it took some minutes for him to swear in? Of course both could resign in mere moments.
The Vice President's job (besides presiding over the Senate) is to become President if there's a vacancy. The swearing is just a formality. It seems unclear whether someone can decline.