When you update an identity with new information (e.g. an updated name, phone number, etc.) using the Desktop Client or Web Console, the metadata for all events associated with that identity are also automatically updated. However, when you update an identity using the SAFR Web API (i.e. PUT /person/{personId}), you must set recursive=true so that all merged identities (and all events associated with those identities) are also updated.
If you see old information after an update, it's possible those people have additional identities in the Identity Database that aren't merged together. You can search for these additional identities in the People Window of the Desktop Client, and manually merge them into the updated identity.