When saving an Events template, the configuration of your events is saved to a ".tst" file. That will not include the actual audio files.
In fact, there should be an "Export" option on that tab, which would export the Events template along with the necessary audio files (exporting everything to a ZIP file). And an "Import" option that would import a ZIP file into your Data Store. This is available on the Layout tab. I should add it to the Events tab and the Chips tab.