I think there are probably several ways that this could be accomplished. But doing a quick google gave me a few options. Mendix can be extended by custom java actions and by the look of this forum post it is possible to call SSIS packages from Java actions either remotely or on local machine.
The other option is that you could expose a service in either REST or SOAP to allow Mendix to call an SSIS service which will run the package.
I hope this helps you. I am not an expert on SSIS, but have some experience integrating it into Mendix. Last time i did it was the other way, so importing data into SSIS using a WebService exposed on the Mendix side.