I haven't had pigs for long, but it seems like every time I've seen truffles, I was in the farm at the time they were dug up. Similarly, I haven't seen any truffles after being gone from the farm for almost the entirety of the day, but I'm not sure if it's a coincidence. So are pigs able to find and dig up truffles while you're not in the farm to see it happen?
Yesterday I collected my first truffle. I had been running around town all day, and discovered it sitting in my barnyard at the end of the day. It hadn't been there earlier in the day when I was on the farm. So, I conclude that truffles can be left by pigs regardless of whether you're on the farm or elsewhere.
Pigs have to be outside. If you check latter you may find truffles even if your are not in farm