Criosphinx

In regard to this ruling:

If multiple copies of "Criosphinx" are in play and a monster is returned to the hand, all copies will activate. It forms a chain, with the turn player's "Criosphinx" as chain link 1.

Does the Turn Player HAVE to put it as Chain Link 1? Can't they pass Priority to their opponent, who can put their effect as Chain Link 1, or pass it back to the Turn Player, in which case he or she would have to put it as Chain Link 1.

Can someone confirm?
 
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