close ALL your windows before double clicking the DMG. Me thinks you are just not seeing where the disk pops open when you mount the DMG (disk image). Quit all application, except finder
once you have all your windows closed open a finder window and double click the DMG. It'll verify the disk and then mount it (which is what you're seeing). It'll then pop up the contents of the dmg which will have an app called install. Adobe application installer will proceed to start and set up your trial version of Premiere. If it doesn't pop up the contents of the DMG you need to go into finder, in the side bar, at the bottom, and find where your devices are listed. It'll show you a disk that says Adobe Download Assistant with an eject sign next to it. Select the name without hitting the eject sign. Now you'll be able to install the software trial.
So what you were seeing was just OSX verifying the disk, what you then need to do is find the disk in finder and open it, if it doesn't open automatically.
I hope tihs helps. Otherwise, there is something wrong with either your os or the download file you have.