Hamsters don't usually store food in their pouches. They use them more as we use shopping bags; to take food away and then stash it in a private place
Not all hammies will move their food about, and hams may change what they do. Mostly my lazier hams prefer to leave the food in their bowl and nibble as they need, whereas my energetic (usually girl) hams will have the whole bowl stashed before I've finished feeding the other hams - a neat trick to get second helping by making me think I forgot to feed them!