Let's say the runner and corp are both at 4 points. The runner is tagged. The runner runs on archives and accesses 3 Quantum Predictive Models and a Restructured Data Pool. This would put both players at 7 points. Who wins?
The runner chooses who wins (and presumably chooses themselves) with the order they access they access the cards. From the Rules Reference:
When the Runner accesses cards in Archives, the Runner turns all cards faceup in Archives, then accesses and resolves each card in Archives one by one in the order of their choosing.
Also, as @LScottJohnson Points out in the comments:
"If the Runner scores an agenda that gives him seven or more points, he immediately wins the game, even if he would otherwise access more cards."
The example in the question and the question from title itself don't really connect, as Zags' answer shows - in that scenario both players never have 7 points simultaneously.
Another similar scenario might occur in a game with Harmony Medtech. While Employee Strike is in effect both players can reach 6 points without ending the game, then if Employee Strike ends, Harmony Medtech ability becomes active again and ends the game in a tie.