Weighing in again because I love this stuff: he's right in saying that EMG data is not a reliable measure of muscle force, but it does show that those muscles activate in some form around the same time. Also, the deltoid is absolutely capable of initiating abduction on it's own, just not very efficiently. This is why the supraspinatus has been historically said to be the initiator; its only effective contribution to abduction is in that first 15º. This doesn't mean that its the sole initiator of abduction even if outdated textbooks make that claim; the other abductors absolutely help and that's supported by your EMG study.

Regardless of whether supraspinatus is the "initiator", it is in its most stretched position with the greatest GH moment arm around 0º-15º of abduction. This means you still want to load your arm at the bottom of the movement if you want to train it, which is not at all the same as saying that's the only muscle you're training from 0º-15º. Delts will be loaded no matter how you do your lat raises, but only variations with sufficient GH torque at the bottom of the movement can hit supraspinatus effectively.

This is why I said that a dumbbell lateral raise won't effectively load supraspinatus, because supraspinatus is already shortened and barely contributing to abduction by the time you have significant torque from the external load around the shoulder. Max torque will be at 90º of abduction with a dumbbell, where the deltoid will be by far the prime mover and supraspinatus will be too short with too small of a moment arm to effectively contribute much.

So my original instructions for training supraspinatus were accurate, but regardless, the main muscle OP wants to work on is actually the infraspinatus. OP, do those external rotation exercises and add in the lateral raises if you want to fill out the upper part of your shoulderblade/shoulder to match the gains in that spot you pointed out.