In 45:9, Yosef finally can't hold back any longer and just has to tell them who he is. He tells them, and then he says, "Go up quickly to my father and tell him that God has made me a king in Egypt. Go quickly, do not delay."
That is the first message he sends? Not "Tell my father I am alive"?
If you heard your friend was in a car accident, and you heard he died in the crash. Suddenly 20 years later you get an email from his saying "Long time no speak. Update - I am president of a major corporation." that would be strange. At that point, you could care less about what job and title he holds. You first want to hear "I am alive." - you want to hear how he survived, what happened, etc.
Yaakov at this point would not care what position Yosef is holding. He would want to hear "I am alive". He would want to hear what happened, how he survived, etc. Only later would he be interested in what Yosef is up to and how he earns a living.
Why is this the message, and specifically the first message, Yosef sends to his father?
I think Yosef is really sending a message within the message. i think he is telling his father that what happened along the way is not important, becuase this was the ultimate goal. Hashem made me king in Egypt so I would be in place to protect the family. Hashem did whatever he did to save me the past 22 years because I was meant to be king. Dad, you can ignore the past 22 years - that was all for the purpose of my being here today as king of Egypt.
The first message is not specifically that he is king, but that his whole life, his whole time away, has been directed by God up to this moment and place. And that is the message that was important for him to send to his father.