That starts once they're sworn in.
If they kill Trump between now and the Electoral College vote, the RNC has the right to submit an alternate candidate to replace him. That would likely be Vance. Then the EC could either vote for Vance, or they could vote for another candidate altogether, since the 'faithless elector' rules would no longer apply (in the case of the states that have them).
If they kill Trump between the EC vote and the certification of the results, the election goes to Congress. The House could chose to certify Vance, but the Senate would have to agree. Since the new Congress is sworn in before the President, what happens depends on who is in the majority in both chambers. The Republicans now have a slight majority in the Senate, and a slightly larger one in the House, so they'd likely pick Vance.
If they kill Trump between the certification of the results and the inauguration, the 20th Amendment kicks in.
Section 3 If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President.