Target Classic has been phased off. Its no longer accessible via UI. If however, Classic API call is made (looks like your organization has been granted extension to migrate off of Classic APIs to Adobe.io), then yes, activities will get created.
Please check out Target API page for the newer way to create activities via APIs through Adobe.io Gateway
I believe there are no side effects of the activities being displayed as coming from target classic. This appear to be happening as your organization has been granted an extension to migrate off of Classic APIs to Adobe.io
I'm experiencing the same thing, however, I followed the steps to create an Offer by setting up the Adobe I/O integration. After generating my JWT and using the curl script, I was able to create an offer via Postman, but like John describes, it's shown as coming from Target Classic. Our organization hasn't used Target Classic since before its decommission.
I should note that, this doesn't appear to cause any problems, as I was able to select the offer from within a test activity. Just wondering what the potential side affects are?