The Mac download is a disk image that contains an installer package. Simply run this to install tintii in the usual fashion. The app will be installed to /Applications/tintii. If you elect to install the plugin, it will be located at /Library/indii.org/plugins/tintii.plugin.
The installer will attempt to automatically detect the location of Photoshop on your Mac and install the tintii plugin there. You should be able to access the plugin via the Filters > indii.org > tintii menu item in Photoshop or Photoshop Elements. If you cannot, you will need to install it manually.
To install manually, locate your Photoshop Plug-ins directory, usually at /Applications/Adobe Photoshop*/Plug-ins. Create an alias to, or copy the /Library/indii.org/plugins/tintii.plugin file into there. Restart Photoshop, and tintii should appear.
The tintii app is also available through the Mac App Store. The plugin is not.