The data in the source field in the metadata section of a record will tell you how the record originated.
Sources
Fulcrum importer
The record was imported into Fulcrum.
Fulcrum iOS/Android
The record was created in the iOS app, after Fulcrum iOS/Android you will see the version of the mobile app used, the OS version, and then details on the mobile device that the Fulcrum mobile app was installed on.
API
The source data is drive off of changesets, talked about in greater details here, and changesets are not required when adding records through the API. So it is likely that the source data will be empty unless you also use the changesets API when generating a record through the API.
Note
The source field is only presented on the Fulcrum web app. It is not accessible in the Fulcrum mobile apps.