Let me completely change the question, briefly. Let's talk about an installation indoors, with a single conduit containing three single phase (two-wire) branch circuits. You have a total of 6 current-carrying conductors in the same conduit. You need to apply the "adjustment factor" (the formal term for the derating factor) of Table 310.15(B)(3)(a). If you are using conductors with an insulation system rated for 90C, then you can start with the ampacity from the 90C column, apply the 80% factor, and obtain a new ampacity. The value you use is either the result of that calculation, or the value in the 75C column (with no derating factor applied), whichever is lower.
That is the essential process of derating. I don't know of any circumstance in which that process would be applied to an underground installation. I am not familiar with the IEEE Brown Book's tables. They have been superseded, and I don't have a copy of the new standard. So I can't speak to how the A/E performed the calculation. I will say, however, that they are flat out wrong about saying you need to derate for underground installations. What you do, as I said before, is to determine what the ampacity is, under the conditions of use. That does not involve the table, coupled with a derating factor.