For .com and .net, updating the account / billing info for the purpose of doing a global whois contact update will often work just fine.
However, for thick registries, such as .org and .us, the registry may still have the old info.
Some registrars, such as eNom, for global contact updates, often neglects to update the whois contact info at the registry level.
So after making a global whois contact update, wait 24 hours, and then check the applicable thick registries, such as .org, .us, .biz, etc to confirm the contact info updated there too...
If it hasn't, then it will be necessarily to manually submit the contact info for each affected domain separately so the update gets propagated to the registry.
Ron