Zapier is not trigerring when form is embedded using the source code.

I tried using the source code and it works but my Zapier integration isn't working with that version of the form...

I have been testing this and I cannot replicate the issue, the Zap was triggered upon submitting the form. 

I would recommend you to check your zap history, this guide will help you doing so: https://zapier.com/help/task-history/ 

You may also run the zap again, this can be done from the Zapier dashboard: 

I hope this helps.