I recently built a new computer with R9 390 graphics card, and Dell P2715Q as monitor. As it doesn't support 60HZ through HDMI, I'm using DP cable.
There are problems. Only way I can get the monitor to display anything on my computer is to set the MST to secondary, and that caps the HZ to 30. Setting it off results in only black screen being shown, though if Display Settings are viewed through second monitor, that shows it being on 60HZ mode at the time. The monitor itself does support 60HZ and cable is fine, as I did test it with another computer that uses Nvidia GeForce GTX 745, and image came through with no problems. My drivers are up to date as well.
What is the problem? I find it hard to believe that R9 390 being much newer card wouldn't be able to do same as weaker, older card.