I'm almost totally sure what's going on here, I'm betting you're starting the stream, then starting the recording, then noticing that the recording takes a while to start up? I changed the way that works, because before it would actually cause major desync, and the bug had to be fixed by forcing the second output started to wait for the next video keyframe, which is typically seconds after. It's not a delay, just has to wait for the next keyframe (if the stream/recording are using the same video encoders).
You can start both the stream/recording at the exact same time and ensure that doesn't happen by using a hotkey and setting the same hotkey to both "start streaming" and "start recording".
I do need to add an option somewhere to make it so you can start streaming/recording at the exact same time without doing that though (so you don't have to set a hotkey).