Switcher Studio has a built-in delay that is minor and deliberate. There is a signal delay of around 200ms (roughly 6 frames at 30fps), which provides a short buffer to allow the Switcher Studio app to synchronize video and audio as well as process the sources for optimal video output.
Delay on playback typically varies for every viewer depending on their internet speed, location and a number of other factors. A 10-60 second delay is typical for most streaming platforms.
Keep in mind your audience will be viewing on their own device and everything will feel real-time for them. This is the same experience with live TV which also introduces a delay, sometimes intentionally to be able to monitor content.
Additionally, when monitoring audio using headphones, you may notice a lag behind the realtime audio. However, the audio will sync with the video output, which you can verify in the Live pane in the Switcher app interface.