The first one is using 'scene-referred' Rec.709, not what you want. The second is using standard full Rec.709, including the display transform.
As to after export, how are you checking that? By reimporting into Premiere or viewing in a player such as QuickTime? Especially, QuickTime player on a Mac?
As that later would show what you're describing because Apple's ColorSync color management utility is more of a color manglement utility ... it doesn't use correct gamma (using 1.96) and also doesn't apply the required display transform.
I definitely used the second settings to work on the graphics, and yes I'm aware of the problem with Quicktime player, that's why I use VLC and import/export the final product on Premiere. Inside Premiere and VLC the color looks as it has to be. But uploading the videos online, the animations look still desaturated. Do you have some other tipps i can check?