I have similar thought, but I think he works for the Founder instead. I believe the Founder knows where the gem is whenever someone holds the gem on their hands, and he sent Thanatos where and who to attack. Also, that's how he can access the hidden server Ogygia, similar like the Praetorians. It's the same reason why Thanatos never attacks the bank guy who hides his gem in his suite nor the Cowboy guy in this episode who also hides away his gem. That's why he soon appears when the Wagner guy takes out his gem to show off. However, it takes time for him to learn the information and travel there, so if the gem holder immediately leaves the area, he's unable to track the said person.