The email you're referencing has to do with duplicate entries, which doesn't seem to be the problem your trying to solve. You also say you're sending new leads to SF through an API connection, but you don't mention if you're using the API or SF add-on. Either API add-on will send data to the target system. Any triggers to send notifications to a user from SF have to be built into the SF API. Triggering an event on the SF server has nothing to do with Formidable's ability to send data to SF. I suggest you redirect this question to s SF API expert that understands if such a trigger exists that can be invoked from a remote system (Formidable). The SF API documentation may also provide a clue.

The Salesforce add-on is not really great unfortunually :( But if you want to use it you can set up a flow within Salesforce to sent a email / notification or whatever when a duplicate is detected.   However until the Salesforce Add-on get's more mature and integrated (which I'm afraid isn't really on Formidable's shortlist) I would recommend to use Zapier or Make instead.  You get a much more stable connection and you can go back and forth between SF and Formidable.  You can then also use a FIND action to check for duplicates based on e-mailadress for example and then either add the lead and send a notification OR to update the lead instead.