As of v9.1, the API does not have any emailing capabilities.

This means that when you use an Action template (either directly, or via a Job Template that contains an Action Template), any Email Templates associated will not be applied, and no email will be sent. 

Email functionality may be somthing that will be included in future releases of the API

A work-around is to use the Priority Manager to send email and apply action templates (which also send email if Email Templates are linked to the Action Template).

1. Create a Priority Manager profile that targets newly created jobs that were made via the API
2. For the action of the Priority Manager, you can send email, or apply an Action template
3. Adjust the frequency of the Priority Manager profile as required.  In this situation, "Once only" may be appropriate