This doesn't seem like a logical workflow at all
And it isn't. It completely invalidates the profile, so you're back to square one. First off you need to realize that there is a fundamental difference between color managed software (Lightroom/Photoshop) and non color managed software. The process of calibration/profiling affects them on different levels.
There are many common misconceptions about monitor calibration, but the most common of all is that it's all about modifying the monitor response to meet a certain standard, and that's it. While this is true in a non color managed situation (it's all the tools you have), this is merely the starting point in a color managed situation.
In proper color management a new level is introduced: the icc profile. An icc profile is a description of a color space. Adobe RGB is a color space, while AdobeRGB.icc is the description of that space. Similar for monitors: <monitor profile>.icc/icm is the description of the monitor's color space. And here's the key to understanding the whole thing: The monitor profile is the description of the monitor in its current (calibrated) state
. Change the calibration, and you need a new profile to describe the new state.
This is the difference between color managed and not. The color managed application uses the monitor profile directly when it displays the image. It's a straightforward profile conversion, although done under the hood and on the fly. The non color managed application just sends the RGB numbers straight to the display. It's calibrated, yes, but the profile has a much higher precision level than that. For a wide gamut monitor this difference is crucial, because only the profile can account for the extended gamut and remap the image RGB values accordingly.
So this explains why it's oversaturated when you view in a non color managed environment. The image is created in sRGB and has sRGB numbers. But the monitor is closer to Adobe RGB.
Now to part 2; how you do this:
First reset the monitor (and video card) to defaults. That part is OK.
Next, the calibration will adjust the video card to reach the desired gamma, white point temperature and luminance level. Here's the thing: You don't want those adjustments to be too dramatic, because the video card is a low-bit, low precision link in the chain. Much better to do as much as possible in the monitor's internal circuitry. That's why the Spyder asks you to adjust brightness.
Then, when the calibration part is finished, the profile is created. This profile, which is what Lr/Ps will use, describes the monitor in its present state. Don't change anything on the monitor from this point
, because if you do you will need a new profile.
(EDIT: I should add, just to cover everything, that the monitor profile is set up on system level automatically by the calibrator. No further user intervention required. I say this because some people will then proceed to set the monitor profile up as working space in Photoshop, which is totally wrong in every conceivable way and defeats the whole purpose).