One common Ashkenazi minhag on Shavuos is to recite the piyut (poem) of Yetziv Pisgam on the second day of Shavuot after the first Passuk of the Haftorah from Chabakuk. The first letter of each line forms an acrostic, spelling out the name of the author, Yaakov BeRabbi Meir Levi, who is commonly identified as Rabbeinu Tam.
I understand that Yetziv Pisgam is for the meturgaman (translator) to ask permission to read his translation of the Haftara and Shavuos is a time to ask permission just like Moshe asked permission to give the Torah on Mount Sinai see here.
My question: What specific link is there between the Piyut and the Haftara passage from Chabakuk?
After all, this Piyut could have been said on the first day Shavuos during the Haftara of Yechezkel just like the Akdomos are said then.