Whose turn is it when the end-of-round 5 turns are called and the turn is being passed?

Question

In the midst of the third game of a match, the active player has just suggested a short cut to pass priority until their turn ends. Simultaneously, the judge announces the end of the round, leaving 5 turns for each game that has not yet completed to attempt to determine a winner. Assuming the opponent hasn't acknowledged the start of their turn by untapping permanents or announcing intentions for "At the beginning..." triggers, which player has turn zero, the turn recognized before the countdown of 5 turns commences?

Answer 1

The turn has not yet ended.

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To end your turn, all players must pass priority until the stack is empty, all players must pass priority once more to end the current step or phase, and then all players must pass priority again if you ever regain priority (e.g. in subsequent steps or phases).^[1]

Since you can't unilaterally end your turn, telling the next player they can take their turn is merely proposing a shortcut to have all players pass priority until it becomes the next player's turn. The others need not accept the shortcut in its entirety, so the turn hasn't ended yet. Only once the last player has accepted the shortcut does the turn end.^{[CR 719.2a-c]}

Having taken no action since your proposal, the other player has not accepted (or shortened) your shortcut (explicitly or implicitly, e.g. by untapping), and it hasn't occurred yet.

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1. There are effects that override these rules. e.g. Sundial of the Infinite

719.2a At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. [...]

719.2b Each other player, in turn order starting after the player who suggested the shortcut, may either accept the proposed sequence, or shorten it by naming a place where he or she will make a game choice that’s different than what’s been proposed. (The player doesn’t need to specify at this time what the new choice will be.) This place becomes the new ending point of the proposed sequence.

719.2c Once the last player has either accepted or shortened the shortcut proposal, the shortcut is taken. The game advances to the last proposed ending point, with all game choices contained in the shortcut proposal having been taken. If the shortcut was shortened from the original proposal, the player who now has priority must make a different game choice than what was originally proposed for that player.

Answer 2

When player A ends his turn, he usually does so by implicitly proposing a shortcut to pass priority through the remaining steps and phases of the turn, which his opponent Player B may or may not accept:

719.2a At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. [..]

719.2b Each other player, in turn order starting after the player who suggested the shortcut, may either accept the proposed sequence, or shorten it by naming a place where he or she will make a game choice that’s different than what’s been proposed. (The player doesn’t need to specify at this time what the new choice will be.) This place becomes the new ending point of the proposed sequence.

719.2c Once the last player has either accepted or shortened the shortcut proposal, the shortcut is taken. The game advances to the last proposed ending point, with all game choices contained in the shortcut proposal having been taken. If the shortcut was shortened from the original proposal, the player who now has priority must make a different game choice than what was originally proposed for that player.

Accepting a shortcut can also be done implicitely, by acting conclusively (such as starting to untap permanents). The rules for shortcuts are largely informal and are subject to mutual agreement:

719.1a The rules for taking shortcuts are largely informal. As long as each player in the game understands the intent of each other player, any shortcut system they use is acceptable.

If no such explicit or implicit acceptance has happened before the judge has announced the 5 extra turns as per Tournament Rules, it is still player A's turn. Should player B dispute that because of a misunderstanding of the shortcut system used by both players, a judge has to be called to decide.