Is Goku aware that he is in the UI state? Based on discussions, questions and answers, Goku achieves the UI state when he is at his limit.
But when he achieves it, is he aware of that?
Does he feel different?
If so, then why doesn't he recreate the changes and feelings to control the state and use it more efficiently?
If he was aware the first time he entered  is kind of unsure, however the second time he definitely was. We see him casually talking with Kefla(she asked him if that was ultra something, he responded its called ultra instinct). Further into the fight he mentioned he is getting the hang of it(meaning he is somewhat in full control) however, as Whis has mentioned it, he still thinks about his attack thus limiting his full potential in the state.
There is still room for improvement in this state, but he is gradually mastering it. I think when his rematch with Jiren will happen he will be in full control.