You don't need to update CIC. As per the following Link:Hi
I received my citizenship certificate today. Should I update cic myself through webform or through my hired immigration lawyer?
https://www.canada.ca/en/immigration-refugees-citizenship/services/immigrate-canada/family-sponsorship/sponsor-parents-grandparents/after-apply-next-steps.html
*******************************************************************************
Use our Web form to tell us of changes in your application, such as:
- marriage or divorce
- birth or adoption of a child
- death of an applicant or dependant
- contact information updates, including:
- phone number
- mailing address
CITIZENSHIP is not part of the list