A nice, brief read concerning transitions and jobs is HERE. To summarize, no, all of those 690 positions are not normally filled by the inauguration of the incoming President - the goal is August for most of them. An exception would be if the incoming administration called for each presidential-appointed position to submit a letter of resignation effective on the date of the inauguration. So far as I know, that's never happened. But if Trump's team did that, then the onus is on the incoming administration to have replacements in place - an impossibility due to the need for Senate approval. But the incoming team hasn't exactly shown itself to be the best and brightest...