This is why Tama-Gos can't die!!
It's not a glitch, just something to make the TMGO even easier to care for. They feed themselves if they feel they will die of starvation (or something). Some think it defeats the purpose of a pet. As a busy person, I actually find it kind of a perk of the TMGO. I'm sure that my Tama-Gos do it occasionally if I leave them alone for a while since I sometimes find them with one hungry heart, even though they've been alone for ages, and should have alll their hungry hearts empty.