Your assumption is correct.

Magnificent! great job!
a word ... when you get that much fast growth, the point of the graft is not all that strong, not strong and woody yet. I recomend cutting it back and letting it branch out, probably 2 or 3 times this season. cut back to 8 or 12 inches. I know it will hurt to do it, but if the whole graft snaps off because it's too heavy and the wind catches it, that will break your heart. I know, because I had it happen ) :
Beautiful work, thank you for sharing the pics.