In the "ILR and Extended ILR" compliance document, the "Employer Details" sub-section under the "Extended ILR" section pulls Employer details from the Extended ILR step in the Onboarding Wizard -which the learner would have entered during Onboarding. This doesn't change when the Employer details are updated on the Edit User screen.
However, the "Latest employment status details" sub-section under the "Individual Learner Record" section will be updated with the new employer details.