There are 2 types of regional contracts, those that end leg 1 and start leg 2 at the same station and those that start leg 2 at another station. The second kind like this contract are the most complicated contract type there is in this game so they are not supposed to be easy.

But it's not as hard as it might first seem to get the train to Noda during the wait, the train will follow your normal signals with Noda as the destination. There are a few things to consider.
First you need to have the Departure sensor on the platform it's on that point towards Noda, Normally you would only have it point towards Fukushima as that's the next station in line but this train doesn't know it needs to pass Fukushima so you need to set the Departure to point towards Noda as well.

Second is when approching Fukushima, if you just have an Arrival sensor it will not trigger for the train because again the train is not actually headed toward Fukushima, In most cases you want a Routing Sensor overlapping the Arrival Senor and pointing towards Noda (and later you will probably get trains that wants to Namba as well) but if you haven't unlocked it yet you can make due with an otherlapping Relay Sensor instead.

Then once the train arrives in Noda you can capture it on the platform with a Stabling Sensor for manual stabling or with a Departure sensor pointing Finished trains towards a Coach Yard if you have those.