Do you have the Auto HP/ Auto MP pouch? You must open your Equipment tab (E) and look at what the pet is wearing. Make sure you are putting the pots you want to consume next to the Auto HP or MP bag. You can also look at this thread on the "Auto Pot" section: https://royals.ms/forum/threads/everything-about-pets.62615/ I don't think this is a bug because I've been using auto hp/mp these past couple of days and it's worked fine for me~
I can at least confirm that auto-hp works most of the time. Occasionally, when I get hits from multiple high-damaging sources in quick successions, my pet does not restore my hp. But the latter is a rare bug and a known one. Also: check to see where you set your "HP alert/MP alert bars" in the OPTIONS. If you set them too low, your pets won't use the designated potions because your HP/MP meters have not reached the warning level yet.