On first thought Camotero I think the issue is that there are a couple(?) Of text references to Epicurus talking about "casting the mind" such as in his figurative journey through space, and so that tends to get picked up by commentators when they see something about "applying the mind.". Pretty clearly Epicurus stressed that thinking requires action of the mind applied to observations, and I don't think there is much more to it than that. The bottom line for me would be that we don't often need the full details but we do need the overall outline in order to apply our minds in an organized way to figuring out problems consistent with the overall view. You could reverse that and say you are applying the principles to the problem but I doubt that makes much difference.
Maybe you are asking something else?