If you cast Karn's Temporal Sundering from your hand, it triggers Taigam. If the spell resolves, it is exiled through rebound.
When rebound would have you cast the card again on your next upkeep, you must control a legendary creature or planeswalker to do so.
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No. Rebound works by exiling a spell that would otherwise go to the graveyard, so if it would never have gone there then Rebound doesn't apply.
Quote from Magic Comp Rules »
702.87. Rebound
702.87a Rebound appears on some instants and sorceries. It represents a static ability that functions while the spell is on the stack and may create a delayed triggered ability. “Rebound” means “If this spell was cast from your hand, instead of putting it into your graveyard as it resolves, exile
it and, at the beginning of your next upkeep, you may cast this card from exile without paying its mana cost.”
702.87b Casting a card without paying its mana cost as the result of a rebound ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.
702.87c Multiple instances of rebound on the same spell are redundant.
And easy way to think about it is to consider Taigam appending "Rebound" to the end of the spell's text. You follow the instructions on a spell in order, so when you reach the instruction "Exile Karn's Temporal Sundering", you remove the spell from the stack and it can't do anything else. It never reaches the Rebound instruction.
When rebound would have you cast the card again on your next upkeep, you must control a legendary creature or planeswalker to do so.
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