The date stamps and user in the activity stream are different for the instances.
The activity stream shows only one user made updates.
While you are cloning the instance, if you Exclude Audit and Log Data, the audit data will not be carried in to the destination instance. So you will find a difference between the date stamps and the users in the activity log different in both the instances. This is the expected OOB behavior.
Recloning the instance and make sure to include the audit data and the log data.