One of the more straightforward ways to help him with this is simply to have him do lots of practice tests, so he increases familiarity with the format. You might also try sitting next to him while he takes a practice test, for a couple of purposes:
1. Initially, just to observe his behavior, to get a better sense of what factors affect his ability to demonstrate his skills. Is he impulsively clicking multiple choice answers before reading all of the options? Is there a clock running on the screen that makes him feel like he needs to race through the items? Conversely, is he spacing out and running out of time to complete the test? Does the digital format interfere with his routines for checking work, or for completing items out of order and then going back to fill in skipped items?
2. Once you have some idea of possible interfering factors, review your observations with him, and ask him if, on reflection, he agrees, or if he thinks there are other factors that might affect him. Together, identify a couple of the ones that are either relatively easy to address, or impact him the most.
3. Now try sitting with him when he does some practice items, and simply pointing out to him when one of those behaviors occurs. You probably won't have to (and probably shouldn't!) sit through a whole test doing this. A few minutes should be sufficient. Whether you try this will also depend on your DC's temperament, as some learners would be rather aggravated by this exercise. The idea, though, is to increase awareness of the difference between behaviors that are helpful to the test context and those that are less suitable, and to give him a chance to develop strategies that work for him. It might be less annoying if you put a sheet of paper next to him, and simply put a tick mark down every time interfering behavior occurs, without comment. I'd let him try first, and then offer additional suggestions only if he seems to be looking for them.
4. If he's amenable, you could then choose a couple of simple strategies to try, and then do another round of practice problems, but this time with the plan to cue him to use a strategy every time you see the off-task behavior starting. Again, he might find it less intrusive if you decide on a silent cue beforehand (like a check mark, or a single word or doodle on the paper that will remind him of the relevant strategy).
There's also another possible interpretation, which has to do with the adaptive format of the digital administration. He may have pockets of higher-level skill that he's acquired (likely on his own), interspersed with gaps (likely due to his instructional experience not having caught up to his ability). On the paper administration, he has access to every item, including the highest-level items, so if he happens to have some discontinuities in his skill development, he can still get credit for those focal strengths, even though he hasn't been exposed to some of the intervening skills. On an adaptive test, the first time he hits an instructionally-based lacuna, the test will shunt him to lower level items, and he'll run out of items before he works his way back up to the higher-level skills that he actually has. It's something one sees in individually-administered adaptive tests too (including nearly all gold standard cognitive measures), which is called a double ceiling (or a double basal, on the lower end), where a student triggers the discontinue rule, but then (if allowed to continue) goes on to complete a string of higher-level items correctly. While one can't formally count all of those extra correct answers, they are clinically interesting.
In the case of the SAT suite specifically, they appear to use a hybrid adaptive model, which means that the digital tests each start with a routing module, which every student completes. Performance on this module determines the next item set, which is not internally adaptive, from what I can tell. If he flaked in some way during the routing module, he would not be presented with the highest level second module, and would be capped on his performance.