Associação entre antagonistas em Homem de Ferro 1 e Homem de Ferro 3

Desde que o OP disse que ele está aberto a respostas fora do universo do filme, aqui está:

The Mandarin is portrayed as a genius scientist and a superhumanly skilled martial artist. However, his primary sources of power are ten power rings that he adapted from the alien technology of a crashed space ship. Each ring has a different power and is worn on a specific finger. From Wikipedia

Então, o grupo terrorista Dez Anéis em Homem de Ferro I, foi uma referência para isso:

The Ten Rings was a shout out to Iron Man’s archenemy in Marvel Comics, the Mandarin, and refers to the literal ten rings that the Mandarin wears, rings with alien origins. From screenrant

Agora, o curta-metragem All Hail the King diz que o verdadeiro mandarim existe:

Ben Kingsley reprises his role as Slattery in the Marvel One-Shot short All Hail the King. In this film, Slattery is an inmate at Seagate Prison being interviewed by Jack Norriss, a filmmaker documenting his life. However, in a plot twist, it is revealed that Norriss is a member of the real Ten Rings organization led by the real Mandarin, and that they are angered by Killian and Slattery making a mockery of their beliefs. He kidnaps Slattery from the prison, telling him that the Mandarin wants to meet him. From Wikipedia

Eu não sei se eles planejam o Mandarim para ter aqueles anéis literais de poder de outro planeta, ou apenas a organização chamou os dez anéis como uma referência para os quadrinhos.

Existe certamente uma relação entre os dois. Embora se possa considerar a menção dos Dez Anéis em Homem de Ferro 1 como um ovo de páscoa para os fãs, parece que os cineastas sempre admitiram que os Dez Anéis e o mandarim real existem neste universo na tela.

SPOILERS ABAIXO

Do curta-metragem All Hail the King :

Jackson Norris: I'm not the one that's going to kill you Mr. Slattery. I'm here to break you out.

Trevor Slattery: That's... nice?

Jackson Norris: Not really. You see, there's somebody who wants to meet you.

Trevor Slattery: Do I know him?

Jackson Norris: No... but you took his name... and now he wants it back.

Quanto à relação entre o mandarim e os dez anéis, este excerto do Wiki da Marvel explica um pouco sobre a sua história mútua.

Discovered by the Mandarin in China’s “Valley of Spirits,” the Ten Rings of Power are actually the product of the dragon-like race Axonn-Karr (or Makluans) from the planet Maklu-IV. The Axonn-Karr utilized them mainly as the power source for their interstellar craft’s engines. The rings’ functions currently cannot be explained by modern Earth science.

The Mandarin learned how to utilize the rings for own personal use and make them respond to his personal commands.

e depois

The Ten Rings is the name of the terrorist organization that abducts Tony Stark in Iron Man. The organization's name and iconography was later appropriated by Aldrich Killian who falsely claimed that he was their leader, The Mandarin, and placed blame on the group for his illegal activities.