No. If you choose to save your credentials in the RSBot client, they are stored locally only and encrypted. They are not transmitted to our servers at all.
More than likely, you are infected with some form of malicious software - a keylogger probably - or you used the same email/password somewhere else that was taken in a breach.
Download and install Malwarebytes. Run a complete scan. This will remove any malware.
Change all of your passwords. Not just RuneScape related passwords, but EVERYTHING. If you were keylogged, then all of your accounts are compromised.
Enable two-factor authentication wherever you can, especially your email since that can be used to steal other accounts.