The key's passphrase serves one very important purpose - and is needed for any use of your private key. Your private key needs to be protected from anyone else having access to it, but it has the additional protection of being encrypted. The passphrase is hashed to produce the symmetric key that your private key is encrypted to.
When you change your passphrase, it only changes the passphrase for the private key that is actually on your keyring - it can't re-encrypt copies of your private key that have been copied to other locations. Since those other copies have not been re-encrypted, those copies of the private key are still encrypted to the old passphrase, and therefore will still be decrypted by that old passphrase. You should either change the passphrase on those other copies, or delete them and replace them with a copy of the changed private key.
An option you may want to consider, to make sure that newly encrypted files cannot be decrypted by copies of your key that still has the old passphrase, is to also create a new encryption subkey when you change your passphrase. This key can then use the new encryption subkey to encrypt files, but can still also decrypt prior encrypted files.