Punakea uses OpenMeta, which is an emerging tagging standard used by a lot of other applications for tagging, e.g. Leap, Deep, Default Folder X, Tags, and more.
OpenMeta uses a file system feature called 'extended attributes' (or 'xattr' for short), that allows arbitrary data to be stored alongside a file, very useful for metadata. Data stored in a special xattr domain is indexed by Spotlight, which is then used to find tagged files. You can see which xattrs are on a file by executing the following command in the terminal:
xattr -l /path/to/file
The data in the Spotlight DB can be accessed by the following command:
mdls /path/to/file

Only if you want to benefit from the Mac App Store and use Punakea's new features like full-text search and tagging on mounted and network volumes. Of course, you can also stick with your current version! Unfortunately, there is no easy way to transition everyone from our old serial-based licenses to the Mac App Store. However, to make the transition less painful, we added several new features, cleaned lots of code, and improved the user experience. Moreover, we cut the price down by 40%.

You have to select a tag by clicking it. If your tagged files still do not show up, make sure that Spotlight is working. You can do that by searching for the file using the OS X Spotlight search panel on the top right of your screen.

Have a look at this article in the Apple knowledge base, which describes a method to rebuild the Spotlight index using the system preferences. For those of you who are more inclined to work on the command line, your can simply open your terminal and execute this:
sudo mdutil -E /path_to_volume