I think it's consistently the case that for clear the bench time the sim pulls your 5 or so players with the lowest total mins for their season - why Barry and Wright play more than planned - but that there's also some preference for the players who are listed at the bottom of depth charts. If the depth chart didn't matter at all my W3 Beal would have never played a minute - that Beal has never been "given" a minute and has quite high total mins but is still seeing some garbage time, 4-5 minutes in 4 different games, presumably because he is bottom of one depth chart.
The two priorities seem to be how many total minutes the player had on the season, and where they are on the depth chart. I don't know why total minutes is weighted so heavily, maybe it was a lazy way to implement garbage time logic into the sim, but it's definitely a major component. I ran a small test to compare these two factors by looking at minutes over expected for my low minutes players (the lowest 6 MPG on each team) in Savage this year, I got 2.4 MPG. I looked at minutes over expected for players who were slotted at the bottom of depth charts, and got 1.1 MPG. Admittedly, a lot of caveats like small sample size, team management changing a bit, and so on, but the ratio has been consistent across teams this year, and matches my expectations from previous seasons.
So while I don't necessarily trust the precision of the numbers, they're not made up at least. I think there's too many variables like foul trouble to suss out the full clear the bench logic without looking at the engine itself or running some fairly labor intensive numbers crunching over a large number of seasons - it's particularly tricky to track variations from game plan since your "target minutes" isn't recorded anywhere and also varies mid-season. But once you know what to look for you can proactively plan to only give 15 TMs to the 17-18 Delon Wright with 17.5 min/82, for example, since that seems to be roughly the right equilibrium with an aggressive clear the benches strategy.