Ace used the twilight traverse to increase his speed to the limit as he made his way toward the exit of the tunnel that Cyrus had just opened. Although he was curious about the identity of that mysterious 'Heaven's Advocate' and how things might turn out for him once he met the overseers, he had no plan of wasting this chance to slip away while that guy drew the overseers' attention.
However, for some reason, the name 'Heaven's Advocate' gave him a very bad feeling because of the 'Heaven' in it, just like the title Heaven's Stealer. Nonetheless, he might never hear or see this person again, so he put this in the back of his mind and focused on the path ahead.
Ace finally saw the light on the other side, and he was elated since this meant he was finally out of these damn mines, and his first experience after his ascension was extremely dangerous.