Thanks for comments. See responses below.
I'll address them below, but I suggest you also add an item to your tool tabs menu:
Select View>Add Tool tab>Quick. That will allow you to quickly get the most relevant settings in view, and the settings in the ball park (see attachment).
Odd light balance?
Yes, I expect the browser to respect light balance in raw file.
Well, LR doesn't do that either really, it compresses highlights and uses an under-the-hood exposure multiplier which is different for each camera model, and converts to an output referred colorspace, to name a few. C1 on the other hand doesn't do much of that, so it pretty much displays as shot, which may be quite different from what you thought but, by not hiding it for the user, that does offer an opportunity to change your shooting style to get a better starting point, if necessary.
As you can see on my attached Quick menu tab, I start with selecting my default style for the camera at hand. I don't remember, but you may need to add that selection yourself. C1 has user adjustable menus for whatever works best for you.
Some cameras allow a choice between several profiles.
I then make sure the Linear Response Curve is selected, and if necessary upgrade to the latest Raw conversion engine.
Next you can select the colorbalance, either from a preset, or from clicking with the eyedropper tool. Don't for get to reset your mouse pointer to the hand tool or one of the others, to avoid accidentally changing the color balance when you later click in the image again.
Double click on tint? Why? Or are you selecting the slider, or the text box? Yes, Lightroom resets sliders to default on double klick. I thought C1 might do that too. It seems to reset both color temperature and tint.
On my system, selecting the tint doesn't change the Kelvin, unless I accidentally
scroll my mouse wheel while hovering the mouse pointer over that slider.
I noted that it chooses Phase One P45+ Flash as standard profile but it seems identical to outdoor profile. Yields exactly the same average Delta E.
I also noted that it defaults to Film Standard, and I usually set it to "linear", but I feel defaults need to give a workable baseline.
The White Balance tab has its own reset button at the top of the tab, but you can also temporarily switch the settings off/on by first holding the [Alt] key on Windows, or I suppose the [Option] key on Mac, it is different from LR so do not try to use that functionality but learn how it works in C1 before blaming it for strange behavior.
As I indicated before, you can set your own default(s) for Film vs Linear curve, and many other settings if you prefer that. That includes Contrast/Brightness/Color settings and many others, like Noise reduction and Clarity and Curves, you name it. All will be set to your preference(s) when you select that(those) saved Style(s).
When you find that you repeatedly need the same approximate adjustments or style settings, save them as a personal default.
Perhaps you note that there is a clipping indication on the flagpole?
If I reduce exposure it's still stays on.
RawDigger says no clipping, even if I actually there is some, visible with log Y-axis.
Capture One assumes the photographer knows how to expose his/her shots, so only an output clipping indication is available. Capture one does allow to set your personal definition of that (output) clipping (after all corrections, like White Balance, exposure corrections, sharpening, etc.) to avoid issues e.g. when printing. You, as a user have full control and can set that output clipping indicator level in the preferences. You also need to set your View>Proof Profile setting for a reliable output preview.
Hope that gets you going in the right direction.