The last updated value is retrieved from the _ts property that Cosmos DB sets; as documented here. This property is deserialised and is available in the raw seconds (LastUpdatedTimeRaw) since epoch and a human readable format (LastUpdatedTimeUtc). Both the base classes FullItem and TimeStampedItem contain these properties.
The CreatedTimeUtc time property available in both the base classes FullItem and TimeStampedItem is set when CreateAsync is called on the repository. However, this property can be set prior to calling CreateAsync in which case it wont be overwritten; allowing you to set your own CreatedTimeUtc value. This does mean that when using existing date the CreatedTimeUtc property will be null.