Here is a suggestion that can help narrow down the problem.
You can flash your controller with OnStep 4.24, then try the same scenario that causes trouble.
If you do not see the problem, that says the problem is in OnStepX.
If you see the same problem, then it is a problem elsewhere.
The only limitation here is whether your controller supports OnStep 4.24, or supports OnStepX only.
That is not how it works with INDI/Ekos and OnStep (4.24).
It does what you expect it to do.
I use the "Sync" function to compensate for the initial Goto errors, and the "Slew" to center the object perfectly before imaging.
One thought: do you have backlash in the gears?
In my case, there is backlash, and I got OnStep to compensate for it (~ 160" for RA, and ~ 30" for Dec).
If you have significant backlash, and you don't compensate for it, the motors will be turning for a while but there will be no movement, and could lead to symptoms similar to what you are seeing.
> After turn on the controller and connect to kstars, the mount already
> unparked, I do not have to press unpark.
I don't use Park/Unpark since I don't have an observatory, so I am not sure
if what you describe has always been the case for OnStep, or something new
> The position always set to NCP (though the scope is parking horizontally).
This tells me that something is not right.
Ask in the OnStep mailing list if this is how things are supposed to work or
there is an issue somewhere (whether a bug in the firmware, or the steps
of your workflow).
> By "reset" what I meant was power cycle.
> After I turn off and on again the controller, the error number return
> to zero in the alignment module
Do you do a Park before you turn off the power?
Do you do an Unpark after you power on?
If you don't then the alignment corrections will not be loaded from NVRAM, and they will be zero.
Doing a Reset is most likely the problem you are facing.
I am not sure about OnStepX, but in OnStep, when you do a Reset (:hF#), all the alignment correction data is zeroed out.
The only way to preserve the alignment data is to a) save it to NVRAM, and b) do a Park.
Next session you do Unpark, but never Reset.
You can verify that by checking the corrections in Azimuth and Altitude: they will have values that are not zero when you finish your alignment, and if you Park/Unpark. But if you reset, they will be zero.
Doing a reset causes OnStep to forget all alignment data.
That, and the NV save failure is probably why you see no improvement.
How to know the mount model is active?
There should be error corrections for Alt and Az.
:GX02# (Azimuth correction)
:GX03# (Altitude correction)
The phone app shows that info too, as well as in INDI.
INDI has plenty of focuser/rotator support.
A full list is here (two pages).
MyFocuser Pro is open source and open hardware.
Don't know if it has rotator support or not. Check the links in the page.