I just followed the suggestion of opening Parallels by clicking on the desired virtual machine's icon in the dock instead of using the Parallels icon. That worked for me. I did not see the annoying Control Center window when opening or when changing from other apps to Parallels. the control center did not show even when changing apps using command+tab and going to the parallels icon instead of the virtual machine's one.
Here is my environment: Parallels 11.0.2, OS 10.11.1.
My steps:
1) opened the virtual machine I wanted - Windows 7;
2) right clicked the Windows 7 icon on the Dock and selected options > Keep in dock;
3) right clicked the Parallels icon on the Dock, selected options, and unchecked Keep in dock;
4) closed Parallels;
5) opened the virtual machine by clicking the Windows 7 icon on the dock.
After that, no more Control Center popping up
Note that the Parallels icon will still show up on the dock when the virtual machine is open (as it runs inside Parallels). Just ignore it. If you click on the Parallels icon the control center will show up. If so, close the control center, click on the virtual machine's icon again, and just ignore the Parallels icon once more.
I will post again if the old behavior comes back.
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