Regenerate - Deadly interaction

I am looking for clarification on a specific scenario. I suppose the keywords probably answer my question, but it felt really strange when I saw it in matches so I thought it was worth clarifying:
If a character with Regenerate and a character with Deadly are engaged and the Regenerate character would be knocked out when damage is resolved, they take their regenerate roll, get a character face, and return to the field zone. Do they then have to roll a second time when the turn officially ends, as the Deadly keyword indicates?
Again, it may be a dumb question or an obvious answer. It just seems odd, thematically, to "regenerate" but still be considered to have been engaged with any character.
If a character with Regenerate and a character with Deadly are engaged and the Regenerate character would be knocked out when damage is resolved, they take their regenerate roll, get a character face, and return to the field zone. Do they then have to roll a second time when the turn officially ends, as the Deadly keyword indicates?
Again, it may be a dumb question or an obvious answer. It just seems odd, thematically, to "regenerate" but still be considered to have been engaged with any character.