Reverse rollover (Traditional IRA to 401k) question

I will try to keep this simple.

I performed a reverse rollover in 2022 to prepare for a tax-efficient Roth conversion. My workplace 401k plan allows dollars to roll in from other accounts. Everything I've read states the 401k plans will only accept pre-tax dollars.

Who determines if the money rolling in is pre-tax? Is this tracked by the IRS somehow? I asked the broker and they told me they assume whatever amount I tell them is accurate, which I found to be very surprising.

Additional context if you need it... The Traditional IRA account had commingled dollars in it. I calculated the basis of the account using form 5498 dating back to the year the account was created. I subtracted the basis amount from the fair market value of the account on the day I initiated the reverse rollover to calculate the pre-tax amount. I used the pre-tax amount for the reverse rollover into the 401k leaving only post-tax dollars in the account.

FMV - basis = pre-tax