Signal calls and messages are all handled over Signal’s servers. In other words, unlike traditional SMS text messages or phone calls, your phone company should not be able to see any of your Signal messages. Only you and your conversational partners should be able to see the logs of your conversations on your phone. (Hooray!)
One thing to note: If you are an Android user, you can optionally switch between using Signal messages and traditional, unsecured SMS text messages within the same app. See more here: https://ssd.eff.org/en/module/how-use-signal-android. On an iPhone, there’s no such choice; all messages and calls within Signal are encrypted and sent over Signal’s servers.