What browser are you using?
Have you tried downloading the installer only? That way you can install it manually after you quit out of the browser.
Remember that to quit out of a Mac application you have to either go to File-->Quit or use the keyboard shortcut "Cmd-Q". Closing the window will not necessarily quit the application as it does in Windows. If you still see the icon on the dock and you hadn't placed the icon there, then it's running. If you did have the icon already on the Dock, check for a little black triangle underneath the icon. If it's still there, then the application is still running.
Good luck.