Chronobot — ruling 1

Untapping your permanents occurs in the untap step, and drawing a card occurs in the draw step. Neither of these are affected by Chronobot’s theft of time.

Chronobot — ruling 2

While it’s your upkeep during your opponent’s turn, you’re the active player. However, any rules or effects that check whose turn it is will still know that it’s your opponent’s turn.

Chronobot — ruling 3

If Chronobot enters the battlefield during an upkeep step, its effect doesn’t affect that upkeep step. Similarly, if Chronobot leaves the battlefield during an upkeep step, its effect doesn’t expire until the upkeep step is over.

Chronobot : règles, fonctionnement et interactions (MTG)

Chronobot is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

When Chronobot enters, switch upkeep steps with target opponent for as long as it remains on the battlefield. (You take your upkeep on their turn, and they take their upkeep on your turn.)

How it works : Chronobot

Original English text — Wizards of the Coast / Scryfall

#1November 12, 2019· Wizards of the Coast
Untapping your permanents occurs in the untap step, and drawing a card occurs in the draw step. Neither of these are affected by Chronobot’s theft of time.
No other card is named in this ruling.
#2November 12, 2019· Wizards of the Coast
While it’s your upkeep during your opponent’s turn, you’re the active player. However, any rules or effects that check whose turn it is will still know that it’s your opponent’s turn.
No other card is named in this ruling.
#3November 12, 2019· Wizards of the Coast
If Chronobot enters the battlefield during an upkeep step, its effect doesn’t affect that upkeep step. Similarly, if Chronobot leaves the battlefield during an upkeep step, its effect doesn’t expire until the upkeep step is over.
No other card is named in this ruling.