Great; let's take it one step at a time.

"Client rolled over all of his Traditional IRAs into Employer 401K."

That means tax deferred amounts are still tax deferred.

"Then, opened a Non Deductible Traditional IRA, and immediately converted to a Roth IRA from the 401K."

But again, that sentence is two Different Things. What you stated here is the same as: I opened a can of Tuna and made a Ham Sandwich. I seem to have skipped over what happened to the Tuna and you don't know where the Ham came from.

Step 1: Opening an Account is what you do for investing.

Step 2: You designate it as your regular savings or investment account or a Traditional IRA (personal retirement account) or a Roth account or a 529 account.

Step 3: You Deposit to that account. The Contribution you then put into that account is either Pre-tax or post-tax or from a rollover and is either trustee-transfer or goes through you or is directly from your funds on hand; and had withholding or not.

You describe the person put personal, post-tax (nondeductible) funds into their Trad IRA account. Everything here, for the Traditional IRA, has no bearing on the 401(k) and is not impacted by having an employer plan.

"Conversion did not come from "new" money."

You have to tell us:

The money that went into the Traditional IRA account came from where?

The money that went into the Roth IRA account came from where?

Once he put money into the new employer plan (the 401(k) account) is that money still there or did he direct them to do something with it?

"It is my understanding that the pro-rata rules (and Notice 2014-54) also apply to the 401k with a slightly different allocation method."

This point is moot if he rolled/converted all of the money in the Trad IRA to the Roth. You told us it was right away and all of it is Basis.

Don't mix the 401(k) into this, unless that applies. And if it applies, how does it fit into the movement of funds?

"Since there is no basis in the 401k, the converted amount is taxable."

A Roth conversion from a Trad IRA is based on Trad IRA, SEP and SIMPLE IRA. Having a 401(k) has no bearing on Traditional to Roth conversions.

I still can't tell where money started, where it went Next, and where it ended.