I realize there is some confusion on this point, but it isn't without reason. Because templates are just a way to load/save a portion of a tournament, this has always been a little awkward. To work around this, if you've loaded a template and then press the "Save Template" button, the "Save As..." dialog will default to the same filename. So, at any time if you want to know what template you're "working with" (which is slightly misleading, too, since you're really just working with a portion of a tournament), you can press the "Save Template" button and see (you don't have to actually save the template).
There are several design issues that have to worked around when deciding how to deal with templates. For example, if using a Rounds template, for example, should the actual level configuration be saved with the tournament, or should it just be a "reference" to the template? Or, what happens if you've loaded a prizes template, a rounds template, and an events template, made changes, and then decide to load a tournament? Does the software prompt you to save each one in turn before allowing you to load a tournament? (Pretty annoying.)
I am interested in revisiting this, though. I'm going to look into it a bit more.