The copy that Double Vision's ability creates is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger
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, : When you next cast an instant or sorcery spell that targets only a single opponent or a single permanent an opponent controls this turn, for each other opponent, choose that player or a permanent they control, copy that spell, and the copy targets the chosen player or permanent
For example, you can't cast a sorcery with spectacle during an opponent's turn unless another effect allows you to do so, even if that player has lost life this turn