Using the Save/Load triggers you should see a modal xf:message for each submission event.

When tested with formsPlayer 1.4.3.1038:

When saving data WITH METHOD="PUT", no 'xforms-submit-done' occurs. Saving data with METHOD="POST" works OK. Loading date with METHOD="GET" works OK.

When tested with formsPlayer 1.5.1.1023:

xforms-submit-done occurs for all submissions.