Yeap, but ID trains IS. Thats what happened to me today. My routine is:Train 1 skill until all 5 of my trainees get a pop up. Then next skill etc.
For the big men trainers. Dont forget to train JS some times. Its a very nice 2ndary to have and relative easy to train. Also it trains IS too. Actually when i have trained JS 1 of my players got double pop up. JS/IS