If my memory is correct, the territories you have with train stations on them must be connected by other territories, no matter the distance between the train stations. To my knowledge, it's the only prerequisite. So, even if on the same continent, if your territory is cut in two, you have... well, a separated network.The point of train stations is to mainly to move troops faster than money lost value during the Weimar years, so...

Oh, by the way, the visuals can take some times to update. Are you sure you cannot move the troops between all for of your train stations ? The pathfinding choose the fastest way to go, and if they use the rail network, it's usualy fairly easy to notice due to the small twists and turns of railway connections.

If neither of this help, I suppose a screen on your part could be usefull.

Aeram wrote:
the territories you have with train stations on them must be connected by other territories, no matter the distance between the train stations. To my knowledge, it's the only prerequisite.

This is most likely the OP's issue. You need a chain of rail-connected territories.

However, I noticed in a recent game that rail links can sometimes be limited by terrain. Trains can't scale cliffs (sensible enough!). It's uncommon but possible that two adjacent territories are separated completely by cliffs, in which case train stations won't connect. Or a station may be placed in a portion of a territory that's cut off by cliffs even if the border between the territories is clear.