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That's kind of a weird scenario if there are two time-until-failures simultaneously running but one of them will never be reached.
If Bob always dies within 6 turns regardless of the player's actions and there's no way to stop it (without completing the mission), then it still feels like purely a Timed Mission, just with some junky information given to the player.
If there's a way to protect Bob for longer than that, then it's just dual objectives like you have linked to.
Although I don't think it applies here because Bob's life is on a timer, a truly pointless timer mission is an Overly Generous Time Limit. That would be more appropriate for a situation like "Mission must be completed in 15 turns, and average players only need 3 turns."
Edited by KD
Bob dies from heatstroke, in turn 2 bob take 5 damage and have 65 hp but the damage from heat increase 5 each turn, (yes you can heal that but it wont last long so completing mission asap is more better)
mission: must completed in 15 turn or less Bob: Dies in 6 turn or less
Edited by Baolen2445