After HDR-SDR tone mapping, too bright

I tone mapped a video, but then I get too bright video. Here is a compare: https://diff.pics/bjIDf8evevzC/1

What can I do for get normal colors, like the SDR BD?

You have to go scene by scene and manually adjust it with Resolve grading tools.
You can also try to play with Tone Mapping/Luminance Mapping settings in Gamut Mapping filter.
It will never be perfect without human intervention though.

I tone mapped a video, but then I get too bright video. Here is a compare: https://diff.pics/bjIDf8evevzC/1

What can I do for get normal colors, like the SDR BD?

It seems there is more than tone mapping going on, the "tone mapped" image is deformed wrt the original.

Could you upload those two original frames completely unprocessed (i.e. no color science, no adjustments or OFX) as DPX files?

As Andrew states, tone mapping won't be perfect.
There is no one-fits-all solution.