You are supposed to be able to do it after adventuring in nature, not only to gather food, but for basic shelter from elements to avoid fatigue. I believe intent is that the 8 hours of adventuring are meant to be included within the Downtime Activity's 24 hour duration, otherwise one couldn't use it to avoid fatigue after 8 hours adventuring in wild. So I don't think you're strictly making the Subsistence check while in Exploration mode, the Exploration mode just doesn't impede the 24 hour duration (although you take -5 penalty for this).
It seems there is vagueness on how long Subsist actually takes when using -5 option after Exploring, since in this case you aren't actually spending entire day. Downtime activities are premised on spending entire day and seem to presume normal rest duration 8 hours, so subtracting 8 hours of Exploring and 1 more for daily preparations leaves 7 hour maximum, but it doesn't inherently need that full length of time, we just don't exactly how long it needs (AFAIK).
It does seem relevant to know specifically how long it takes (in post-Exploration "-5" mode), since when you start sleeping and how long it takes to build "camp" depends on this. It also seems plausible that WHILE Exploring you could be opportunistically gathering berries or sniping deer as your Exploration activity, which could nullify or reduce the time requirement for Subsist. If you did this continually for 7 hours of Exploration, I'm not sure if Subsist would be considered to have been completed without further time need, or you could qualify to ignore the -5 penalty since you were Subsisting for entire duration NOT after hours of fatiguing non-Subsist activity.
That's just my take, and I'm not sure if I'm missing something on it, it would be nice to get clarity.
I guess what I really want to know is:
Are subsistence rolls something you are supposed to do every day, even in exploration mode, when you do not have food and shelter readily available?
Does anyone know the answer to this?
I believe so, if you can't or won't consume rations you already have.
I would generally not think about it as hard as Quandary did for how that works out logistically, in the same way that I don't sweat when meals are taken during 8 hours of travel. I'd say the assumption is that the -5 penalty represents you not devoting extra time to it at all, or not enough to significantly impact travel or other exploration schedules. Instead it is more about if you can find food along your path.
For example, maybe you shot a rabbit that happened across your trail. Taking the time to skin and eat it isn't that much longer than the time you would have stopped for lunch anyway.
It may also help to remember that adventurers aren't punching a clock. Spending 8 hours working, 8 hours sleeping, and 8 hours "in between" doesn't mean it is exactly 8 hours on each spent everyday. Just that is what the average is.