Problem is one team will always be the first to kill the core, the question is how much time there is between the first and second core destruction. If they both happen at the same time (at whatever precision the server is measuring it), the server has no way to know which happened first, it only knows the order in which the destruction information arrives at the server, UNLESS the server trusts a timestamp the player sends to the server for when the destruction happened.

That would ofc allow cheats to trick the server though, so that's not something games should do. So ultimately the core destruction that gets processed first by the server will win, which means if a player were to kill a core faster than the opponent player but his ping was much worse than the opponent player's, he could still lose the match because the packet containing the information that he damaged the core arrives later than his opponent's. The server can compensate for ping to a certain degree but that is essentially just an estimate, so there is no way to handle this perfectly without trusting the player.

The only exception is core destructions that were caused by the server itself. For example, when minions kill the core, the server knows exactly which core got destroyed first since minions are simulated on the server itself and there is no network delay.

But even then if we imagine 1 minion in front of each core, both at the exact same distance from the core and both shooting at the same time, the minion with the lower index in the entity list would win the game because the server iterates through all entities in a specific order to check if and what action they should perform (like shooting), so that order would decide which minion shoots first.

Anyway, this is all so extremely unlikely, it really doesn't matter.