A power bank that gets too hot when it's charging at full capacity is something you need to take seriously. It's normal for it to heat up a bit, of course, but if it's actually "burning," that's not ideal. When you're charging two devices at the same time from a 10000mAh power bank, you're drawing quite a bit of current, and that generates heat. The problem is that if the internal heat dissipation isn't very good (and some of the cheaper Anker models have that issue) the temperature goes up more than it should. Excessive heat can degrade the internal battery and, in rare cases, even create safety issues.
What I'd do is stop charging both at the same time for now. Try charging one first, then the other, and see if it heats up less. If even charging just one device still gets really hot, or if you notice the power bank smells weird or warps a little bit, that would be a red flag and you should stop using it. Also make sure it's not exposed to direct sunlight while it's charging, because that adds more heat. If it's a new gift, Anker usually has good warranty coverage, so if you're really having issues with it, consider claiming it. For now use it carefully, but don't panic.