For this player at present they wouldnt. However, they would have for Santander and Alonso, both of whom you’ve suggested signing this offseason. I could not tell that this post applied to only one player.
For this player, Kim, he CLEARLY does not want a 5 year deal at reduced annual salary because he accepted a short term deal with an opt out after year 1. His goal is to prove he’s a solid player this year or this year and next year and test the free agent market again. Even if you made the full contract offer a lot richer, he wants to hit free agency again so you’d just be increasing your payments if he sucks or is hurt. Furthermore, by signing with the Rays, he gives himself a good chance of playing competitive games this year and a good performance in those games or in the playoffs could make him more money - in Chicago you’d have to pay a year 1 premium because the only way he’d play competitive baseball is if he were traded, which is disruptive as well.
This fit is terrible from the players perspective, so you better be shelling out a much higher salary in Y1 and your spread out the payment plan shows you didn’t pay attention to the contract he signed.