Do I need to pay the deflect cost of a spell I'm controlling with Rebuttal?

No. Deflect is a cost paid when a spell is played (finalized), and Rebuttal doesn't play the spell — it just changes control of an already-finalized chain item. The original controller already paid any Deflect costs at that time.

If you use Rebuttal's "make new choices" option and retarget onto a unit with Deflect, that new Deflect cost is ignored: Rule 755 says costs "to play" incurred from new choices on a finalized chain item are ignored, since the spell is already played and its costs paid. This matches the general rule that Deflect only applies during finalization — it can't be triggered by a spell already on the chain (Rule 809.1.c, Rule 755).