I want to make sure I get this interaction correct.

Tavson in the Ups can spend a charge when suffering damage to perform an action, and has 2 recurring charges.

If Tavson has 3 hits coming in, a charge can be spent to reinforce after the first damage is suffered. The reinforce will not be active to reduce 1 of 2 remaining hit because reinforce triggers in the neutralize results step and that step is complete.

Did I get that right?

Yup. Checks out!

I concur with @Ryfterek . Like you said, Reinforce adds an evade result (which in turn would cancel a damage result) during the neutralize results step . Damage is suffered after that step is over, so while you would have the reinforce for the NEXT attack, you couldn't take advantage of it here.