I've been trying to wrap my head around this for academic reasons, and to try and better understand the P9570 as I struggle through the learning curve with this printer that I call Epson's dumpster fire. Ultimately I use Imageprint from Colorbyte, so I don't need to know how to print from Photoshop, but there are a lot of important parameters in the EMI and driver that need to be understood.
From what I can see, you could use the ICC profile you want and let Photoshop manage the colors, or you could select "let printer manage colors", but either way you need go into the printer settings anyway and select a paper type, size etc, and then save that as your preset, so you might as well let PS handle the colors now. It's a new way of printing from PS and LR. For years now everyone has recommended letting PS manage the colors at print. But since fine tuning is now only in the EMI and LCD panel settings for things like platen gap, feed adjustment (which is called feed offset now in the EMI), suction, dry time etc, you really need to let the printer manage the colors.
I had to learn this because even though I'm using Imageprint, they had a bug that was not passing information to the printer to override things like feed adjustment, so I had to learn all this and show that their parameters were not getting passed to the driver. I have mixed feelings about moving it to the EMI. I really see no reason why you can't have an EMI manage paper types and pass them to the printer, but still let the driver override those things at print time. Some prints require tweaking, and some problem solving requires tweaking, so putting those settings in the EMI but now allowing the print driver to override them doesn't make sense to me.
I've also found the same issue with the Epson EMI as Canon has with its color management setup, which is similar, and that is that if you have multiple computers printing to one printer, there is no way to use the EMI without constantly overwriting the LCD panel. There is no way to acquire media settings from the printer. The EMI from different computers conflict with each other. So if I go to computer A and download and install settings to the printer, then go to computer B, I have to do it again. For profiles that have updates, there is a "download and install" button. The same is true of Canon. There is no option in the EMI to "acquire media from printer". On each machine you have to "download and install".
I can sit at one computer and remote desktop into two others and see them out of sync. So the computer is not acquiring data from the printer correctly when you start EMI. It's not really bi-directional. The computer sends information to the printer and the printer registers it, but it's certainly not bi-directional as some would suggest.