March of Swirling Mist causes odd behavior in Deep-Cavern Bat
Opponent had used Deep-Cavern Bat to exile two Instants from my hand (until each Bat left the battlefield). Arena displayed each of my instants under each bat as a reminder of this conditional exile. Later I used March of Swirling Mist to phase out the two bats; when this happened, instead of keeping my exiled-until-bats-leave-battlefield Instants under each bat, or returning the Instants to me, the Instants went to my exile zone. :( When the bats phased back in on my opponent's next turn, my instants did not appear under the bats. BUT when my opponent used my bats to block my attack on a subsequent turn, THEN my instants re-appeared under each bat -- and returned to my hand when the two bats died in that combat.
I do not know the correct behavior, but my bet is it isn't this.
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Murdoctor#39989 commented
Same thing just happened to me. When I phased out my opponent's Deep Cavern Bat, the card it had exiled from my hand shifted from appearing "under" the bat into the "exile zone" on the battlefield, then reappeared under the bat when my opponent later assigned it as a blocker. They seemed to be taken aback by this as well, because they unassigned it as a blocker (so I wouldn't get my card back), then assigned it again anyway (because they were going to take a lot of damage otherwise).
Phasing out doesn't count as leaving the battlefield (even though it's no longer "on" the battlefield, it never actually "leaves" the battlefield per the game rules), therefore the card the bat exiled should still be tracked as having been exiled by the bat while it is phased out, and should remain that way when it phases back in... but the fact that it visually disappears from under the bat until the bat is assigned as a blocker is very misleading.