there is no mystery about this because the finnish volunteers served in the prussian Reserve Jäger Bataillion no.27 and take rifles and complete equipment back home. you can say they were voluntary Jäger like this man from the napoleonic war.
this prussian Jäger battalion was more or less the model the finnish army was formed.

you can see such things allways best on the headgear! the 19.century busby so typical for the Jäger became unpractical in WW 1 and was replaced by the moutain cap of the tirolian Kaiserjäger in german jäger battailions too. (the kaiserjäger where moutain hunter regiments)
so the Bergmütze came into finnish service with the finnish volunteers.

Kaiserjäger

Finnish Jääkari