A simple way would be to create a process for that import and include a second import that would set a boolean line item dimensioned by Users list. I created some screenshots to illustrate: Module has a boolean line item, dimensioned by Users, with a fixed boolean to import from and one to set via an action.
Import in to the same module copying the value from TRUE to imported As an end user running the import they only see themselves, so only set against their user...
You can capture the date when the user is importing the data. However, to capture the timestamp in a module you might need to use anaplan connect or hyper connect as Anaplan does not capture the timestamp.
However, now in the section actions the admin can get hold of date and timestamp when a process was executed.