No, you do not. If you read the text of [mwcard=MW1E34]Reverse Attack[/mwcard] closely it says that you reveal it during the Avoid Attack Step and it only changes the target of the attack during the Roll Dice and Damage and Effects steps. Therefore, your mage will not become the target of the attack until after the Avoid Attack Step is over with, and will not get the opportunity to reveal their own Reverse Attack.
RA is a strange card indeed. As per the combat section of the rules:
"If the attack is avoided, skip to step 5: Additional Strikes."
However that does not happen with RA, but from a technical as written view makes RA not function at all unless the RA happens in Step 5 which would allow for a defense to be used. (first thought reaction without fact checking so ingest that with a grain o slat, special edition)
I think iNano might be right here with timing window, since you can reveal before proceeding to the next step but would still hit yourself as attacker never changes, only the target.