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No creatures that player controls will untap during their next untap step, even creatures that don’t attack. This includes creatures that enter the battlefield or become tapped after this spell resolves.
If, during that player’s declare attackers step, a creature that player controls is tapped or is affected by a spell or ability that says it can’t attack, then it doesn’t attack. If there’s a cost associated with having a creature attack, its controller isn’t forced to pay that cost, so it doesn’t have to attack in that case either.
If the opponent exerts any creatures they control, exert and the effect from Imaginary Threats stopping them from untapping both apply in the same untap step. Those creatures will untap as normal in the player’s subsequent untap step.
