Goku got its first triggered power from the spirit bomb because the spirit bomb power is too strong and it somehow clashed with goku power and awaken the limits.

the 2nd time was because kefla getting stronger when fighting goku, saiyan has the ability to get stronger when fighting and injured. So it somehow triggered the ultra instinct again.

besides, they have a few secs of flashback explanation where the beerus assistant was training them and explaining to them about the ultimate evasive skills. I assume these should somehow explain abit about the sudden changes in the ultra instinct...just my opinion =P