If a commander is tucked into the library by an opponent's effect, can its owner choose to move it to the command zone?

Under the current Commander rules, whenever a commander would move to any zone — including the library ("tuck"), graveyard, hand, or exile — its owner may choose to move it to the command zone instead. This is a replacement effect that the commander's owner controls.

This applies to any effect that would put the commander into the library, such as Hinder, Spell Crumple, Chaos Warp, or Oblation. The old "tuck" rule that forced commanders to stay tucked was officially removed in June 2015. CR rule 903.9 (the Commander rules section) codifies this replacement effect.

The choice is made by the commander's owner, not the opponent whose effect caused the movement. So if your opponent resolves Chaos Warp targeting your commander, you decide: do you let it get shuffled into the library, or redirect it to the command zone? Most of the time, owners choose the command zone to avoid losing access to the commander.

Concrete example: Your opponent casts Hinder targeting your Atraxa, Praetors' Voice. When Hinder resolves and would put Atraxa on the bottom of your library, you may instead choose to move Atraxa to the command zone. It will cost 2 extra generic mana the next time you cast it due to the commander tax (CR 903.8).

Note: this replacement effect can be applied any time the commander would change zones — multiple times in a single game if needed — and it is always the owner's choice, never mandatory.