That's a mistake by the fire truck. You aren't supposed to preemptively run a red light to help them, they're supposed to order you to do it right away if that's what they want.

This surprised me, and I haven’t found any information one way or the other about the universality of the rule, but I did find this guide that strongly implies you’re correct.

https://www.firerescue1.com/fire-truck-crash/articles/stop-f...

In Germany you have to make way/not obstruct, though you don't have to endanger yourself excessively. So if the traffic behaves, you absolutely have to move out of the emergency vehicle's way traffic light be damned. Usually you'd pull over to not put yourself into a prime t-boning spot, but with good visibility you actually drive across the intersection to where you where going anyways, and ensure you let them pass.