For example, say I have an espeon with synchronize and I changed her nature from adamant to modest using a mint. Will the wild Pokemon I encounter have adamant natures (original) or modest natures (new from the mint)?
edit: fixed the phrasing (referred to the wrong nature as the original in my example)
Original nature. Mints only change the stats, not the actual nature. You will find more Adamant Pokemon in your example.