Is it correct that every time I start the camera, the scan range is set to Auto?
No idea but there is no reason you shouldn't stick to it. And I mean it as a person who usually hates all the "auto" stuff.

The implementation of the auto algorithm is really smart. It combines ~binary search to find the coarse range with fine sweeping afterwards.
Try to rather not use the +/-100 mode as it sweeps with the step of 5, meaning that the final accuracy is only +/-5. The +/-20 method can also deliver a worse result than the auto if the values of +/-20 are still not beyond the borders of focus confirmation.
BTW, from my experience: I don't find the Dot Tune method the ultimate solution for focus problems. I'm used to still apply additional corrections based on photographing of real subjects and not focus charts. It seems to make a difference... Also the calibration distance matters as lenses can have an error depending on the it... But it's a good starting point and hopefully you don't have to play with the correction further, like I had to. Maybe I just have really bad lenses?