IMO it's important to make sure puppies get appropriate amounts of calcium, so I *would* feed a commercial diet for all life stages (or specifically for puppies). Canned or pre made raw may be easier on them than another kibble.
I do think probiotics are a good idea (human ones are fine -- you can feed them in peanut butter or cream cheese). A bit of canned pumpkin (plain, not pumpkin pie filling) might help.
If it's bad, your vet can give you what is basically a high dose of probiotics (also available online, but I'm assuming you don't have the time) and canned food specifically for dogs with gastro issues (Science Diet has one). Not ideal, but better than having young puppies who aren't getting their nutrients.
ETA: also, make sure they get to the vet for a puppy check up soon, and that the vet does a fecal test. They may also have parasites, which aren't uncommon, and which wouldn't have anything to do with the food.