It might have nothing to do with JR Kyushu but JR West isnt't everything or even the majority of train service in Kyoto. Kyoto has at least 8 train companies, Keihan, Kintetsu, Hankyu, JR West, Keifuku, Eizan, Sagano, and the Kyoto Subway. Japan has over 100. The museum does not appear at a glance to affilated with any particular one - though I only glanced

Kyushu has 16 train companies

The museum is owned/funded by JR West (at least if you believe Wikipedia). It has their logo on the about page https://www.kyotorailwaymuseum.jp/en/about/ .