Are just using the Launcher or have you fully upgraded your accounts into a Jagex Account?
It is possible to be using the Launcher and not be a Jagex Account.
If you have only installed the Launcher and added your accounts to that, there is no need to message Jagex as only the account you request will be deleted.
If you have fully upgraded into a Jagex Account, you will need to cancel the deletion as all linked accounts will be deleted, not just the one.
To check your status i.e. Jagex Account or not, log into account management (click on "My Account" at the top of this page) and look for a blue 'Upgrade' button at the top right under "Enhance your security". If you can see that blue button, you
don't
have a Jagex Account and don't need to worry.