It took some digging to trace back the scripts, but there's a script in this system named "Create New Assignment" inside the Assignment Folder's Action Folder.
This script is the script that actually assigns a task to a contact and it can be modified to add a Send Mail step as the next to last script step.
Refer to the Assignments Table Occurrence box to find how to refer to the correct fields for the data you want to include in the email. The person's email, for example, would be the Assignment_RelatedContacts_ByID::Email and the name of the task would be found in Assignment_RelatedTasksByID::Name_Task.
Worked perfect! Thanks so much!