Upvote:4
When travelling by train there are generally two types of tickets:
In Germany the moment you encounter a delay, when travelling on a discounted, non-flexible ticket your ticket becomes flexible by default. So from that moment on you can just take any train on your route. That is what the conductors in Germany told you to do.
For international connections it is a bit more complicated, as you usually must stick to the same border crossing as the original ticket. You have a ticket that goes via Tantow, but the direct ICs go via Frankfurt(Oder). So you could continue via the same route, taking the next train to Angermunde and connecting there with the Rail Replacement bus to Szczecin, and then connect onwards to Warsaw. But your rights as a passenger are clear: The railways must do whatever is reasonable to get you to your destination as quickly as possible, even if that involves rerouting. So your ticket should be made valid for the direct IC trains to Warsaw as well. They can do that at a ticket office, but a train conductor could help you as well.
For next time: Avoid such complicated, lengthy routings, and avoid overnight layovers at train stations. As you found out these are not really nice places to stay overnight in. You could have done Aachen - Warsawa with only one change by starting on the morning ICE to Berlin...