Especially to the reserved green coach

That is, green cars even on some commuter trains will tilt to face direction of travel at their end stations. You can see it happen e.g. at Tokyo station after a Tokkaido line train arrives, after all passengers exit and the doors close.

For Shinkansen and express trains, this is a given, usually even in second class, apart from the rare reserved compartments, and some airport trains where the space between back-to-back seats is used to store luggage.