Minamo

A face-up plane card that's turned face down becomes a new object with no relation to its previous existence. In particular, it loses all counters it may have had.

The chaos ability doesn't target the cards it will return, so they're not chosen until resolution. As the ability resolves, first the active player may choose a blue card in their graveyard, then each other player in turn order does the same, then all cards chosen this way are returned to their owners' hands. Once a card is chosen, it's too late for players to respond.

A plane card is treated as if its text box included "When you roll {PW}, put this card on the bottom of its owner's planar deck face down, then move the top card of your planar deck off that planar deck and turn it face up." This is called the "planeswalking ability."