I was also expecting Nebula to vanish when she shot her past self and Cap's situation with the aging clearly implied he had lived through the past in the reality that was the base reality of the MCU unless they were implying he lived to the present in an alternate reality then shifted back to the main MCU.
No, I don't think their explanations helped. People just went with it and enjoyed the ride. And I say that as someone who loved Back to the Future 2 and was not confused at all by the details of time travel.