I mean, it's not an order/mandate. You still have to adjust to the game situation. But the analytics department and the two pitching coaches have a lot more to do with the game plan each day, and especially what sort of availability they have (how long, or at all), than Thomson does. And the pitchers know before the game which pockets of the line-up and what possible innings they are likely to be in, and for how long, and with match-up plans that go far beyond L/R these days. It can never go exactly to script of course, unless they are all throwing perfect innings. But I think it's pretty rare, once the starter is out and the first man has come in unexpectedly, that Thomson is thinking, "can I leave this guy in for one more inning?" versus already knowing who the next guy is.
Of course he probably wouldn't have even used these exact pitchers in that order if it had still been 7-1 instead of 7-4 when Strahm entered, though they didn't really have options to eat innings in a loss given how guys had been used and with only 7 arms.
I think the main issue is still the current depth. Strahm is good enough to get guys out from both sides and go longer but he's been essentially the #2 reliever for the most part. Alvarado isn't supposed to be the closer either (only sometimes). Ross is mean to be a middle reliever but has been needed in bigger spots.
I also don't get too worked up about extra inning games. It's fake baseball and most managers don't save their best relievers for 10th innings that may never happen. Last year it was often Soto or Ruiz (before he was proven). Last night it shouldn't have been Alvarado but after that comeback they hoped to squeeze more out of him. If Ranger had pitched longer one more guy would have been available.