HI @JasonC,
Uploading to Kaltura can be done in multiple ways, including KMC, KMS [MediaSpace] or just directly using the API so you'll need to be a bit more specific.
If the upload is done by KMS, the user should be able to see his uploaded assets under "My Media". They will also see any asset that has been uploaded and marked as "Public" by other users. If user A uploaded something and has not made in public, other KMS users will not see it but a person who is set as admin in KMS or KMC will be able to see and if turned on, moderate them.
Hope this helps,