It's also possible that Khan met Chekov shortly after
the events of "Space Seed," but before Khan's people were dumped on Ceti Alpha V. In To Reign in Hell,
I made a point of establishing that Chekov was among the crew members who escorted Khan and his people to the planet and provided them with supplies, said goodbye to Marla, etc.
The simplest explanation has always been that Chekov was already a member of the crew during Khan's takeover, just not assigned to the bridge yet. This seems perfectly plausible to me. How many random crew members did we see every episode, most of whom had never been seen before? Presumably they'd always been there.
I mean, take Marla McIvers for example. She didn't just magically appear on the ship in time for "Space Seed." We didn't see her in any earlier episodes, but I imagine she bumped into Charlie Evans at some point, was affected by the "Naked Time" virus along with everybody else, beamed down to the Shore Leave planet for some R&R, and attended Anton Karidian's shipboard production of "Hamlet" . . . .