I don't speak German unfortunately - I have a deceptive last name !
Thanks for the note, I have a better idea of what is happening now.
There's a few Hype behaviors that I think understanding will help this document. First, you can think of timelines as streams of animations. A timeline is not a particular state - for example you could have a timeline animating up and down, and another timeline rotating the box. Both can be run simultaneously and will not interfere with each other.
So when looking at any given timeline you can't make the assumption what you see in the editor is what will happen on the page as the current view will only show the effect of the animations from that timeline. The question becomes, then what is the rest of the state that isn't animated? Hype will use the state from the playhead of the main timeline in the editor.
The other consequence from this is the question of what happens when two timelines have animations for the same property? In this case the last timeline set to run "wins" and owns animating this property. Otherwise things would bounce back and forth constantly between competing timelines.
So putting this together, I think the way to have your document work is to make the following two changes:
Swap the order of the "Go to time in timeline" and "continue timeline" actions. This means that the timeline with the continue will "win" and you can run those animations free of interference from the main timeline.
Add keyframes for opacity on the element that you want to display. Right now the "Langstrasse" group in the Langstrasse_Tweets timeline doesn't animate in on that timeline. This means it will stay on whatever state it was from another timeline. So you should add opacity keyframes (even if they don't change) to declare that the timeline should use that state. Same with the Altstetten group/timeline.
I've attached a variant of the project with these changes. I can't say it is exactly what you want, but I assume the behavior is more of what you were going for.
project-fixed.hype.zip (326.8 KB)
I hope that helps!