You could do as Brian suggests, or you could have your tires rotated.
Either way, that's the first step in checking to see if there's a
difference. I don't recognize TBC Tempest, so I suspect it's a low-cost
generic tire, which is unlikely to have similar traction characteristics
to your Kumho.
As for the tire repair, it depends on where the puncture is. A puncture
in the sidewall is not repairable safely.
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