On reading the announcement here https://www.ultra-combo.com/eagles-pricing-availability/ the following is mentioned.
… there was a key phrase missing from this announcement. “when the Steam version rolls out.”
Eagle will be free for Killer Instinct: Definitive Edition owners, but since this work was originally scheduled for months from now, we are trying to make it happen as quick as we can.
KI:DE & Season 3 Ultra owners will get Eagle free – but may not work immediately
We wanted to make sure the offering we had on Windows 10 & Xbox matched the offer we were releasing on Steam. To do that, we naturally have to include the 3 characters currently missing from the DE bundle. That work was to be done when the Steam version launched, but a miss in verbiage on-stage led us to our current predicament.
From that, I can only surmise that it will occur when the Steam version is launched, and those who have access to him now are just lucky.