Jonisium use Twitter's API and the standard Oauth authentication. Your Twitter password will never be shared to Jonisium and there is no way Jonisium can read it programmatically.

When you login using your Twitter account for the first time, you will automatically get http://jonisium.com/[Twitter's screen name] website.

If you want to stop Jonisium from accessing your Twitter account, you can remove the access by going to Twitter website, go to Settings --> Connection and revoke JETwit access.