I think that if you change keys with one character (and override the default configuration) you have to "re-apply" the default configuration on the other characters that already existed...
Yes, you need to go into options on each existing character and choose to apply your custom control settings to each and every one of them one by one.
If you want your custom control scheme to apply to all new characters there's a setting for that too (default Key binds for new characters). But if you alter your custom control scheme after creating a new character then you need to re-apply it to that character. The control scheme is basically saved ("snapshotted") per character.
To apply your custom control scheme to an existing character:
Open Options:
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Go to Controls and click "Default":
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Click "Custom":
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Click "Apply"
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To make your custom control scheme apply to all new characters you create:
Open Options:
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Go to Gameplay and toogle the option "Default Key Bindings":
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