Here's what threw me off. At the end of Apocalypse we see people collecting Wolverine's DNA from Weapon X, and the case clearly says ESSEX Co. Which any comic reader would know means Mr. Sinister. But in Logan that seems to have gone right out the window
I can only imagine that Alkali Transigen is only a cover/shell company, since on the case folders it said "Transigen: Pediatric Cancer Study."