Here's what DB says about train-specific travel on saver and super-saver fares:
You may only travel on the long-distance trains (ICE, IC/EC) and on the days indicated on the ticket.
When starting or completing your journey on regional or local trains (RE, RB, IRE, S-Bahn), you are not restricted to specific trains or times. Your journey must be completed by 10 am the following day.