What is the correct way to clean up primary & replica servers?

I am getting conflicting reports on how this should be done.

My assumption is that if I clean up the primary of obsolete & superseded updates when the replicas synchronize, they will update themselves to match the primary.

A PowerShell cleanup script I found had a Microsoft response that said otherwise. The rep said you need to clean up the replicas first, then do the primary last.

What is the right way to do this?