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You would need to export the features in each polygon to it's own separate feature class, then assign privileges for the desired user to each feature class.
The option you mentioned for the replication limits the features that are replicated. It essentially just clips the feature class being replicated.
For a web application, you have a little more flexibility when it comes to editing features when Editor Tracking is enabled. You have the ability to 'Enable ownership-based access control on features'.
This is based on features though, not an extent. This will only allow editors to make edits to features they created. They cannot edit other features unless 'Update' and 'Delete' are granted.