"Since the client added his own funds to compensate for the withheld taxes, and this money is not technically a rollover, what to do with the excess rollover?"

Yes, it is part of the Rollover. If he only made up the difference between Gross and Net, all he did is make the Rollover match the distribution, which is allowed.

"60-day rollover – If a distribution from an IRA or a retirement plan is paid directly to you, you can deposit all or a portion of it in an IRA or a retirement plan within 60 days. Taxes will be withheld from a distribution from a retirement plan (see below), so you’ll have to use other funds to roll over the full amount of the distribution."

From: https://www.irs.gov/retirement-plans/plan-participant-employee/rollovers-of-retirement-plan-and-ira-...

But these should be happening direct or Trustee-to-Trustee. You can only do this once each 365 days. Not per calendar year, but literally by count of days.