I don't understand your problem? When I open an app, it starts on the bottom, but I can move it, where it will stay until I close the app. If I right click and choose Pin < application >, it will stay on the dock when I close the app, and the icon will stay where I move it.
I don't use Mutiny, but I have used the MATE Dock Applet, which Mutiny uses, for a long time. I've seen this once or twice when I opened a large number of apps, so I think this is a flaw in the Dock Applet. I suggest you submit a bug report with the Dock Applet's issue tracker.