Strange, it seems to work perfectly well in practice
Something must be wrong then because if you sit down and draw it on paper, unless the process you describe is commenced from a position where the TMG is paralleling the desired track then simple trig shows that it can't work.
For the method to be valid it must at least in theory get the aircraft back onto track. If it can't do it in theory then the method is not valid because it fails to do what it is designed to do.
For the method to work in both theory and practice, the first step must be to parallel the desired track.
The method is sound. Just the application (as per your exact description) seems to have a minor flaw.
The steps are simple;
1. Deduce track error. and turn by this error towards the desired track.
2. Measure distance off track (this will no longer be an increasing figure).
3. Turn by SCA towards track and hold for time in minutes = distance off
4. When time up, Turn by SCA in the opposite direction to maintain desired track.
Unfortunately, your explanation and the method many are using is to do the following;
Bloggs is 3nm right of track with a 10 degree error.
Bloggs turns left by SCA and hold this for 3 minutes.
Bloggs think that they are back on track but they are not. They are 3nm to the left of the track they they had been flying.
Let's use a method that really does have the potential to get the flight back on track.
As I said, draw it on paper and see that the TMG must parallel desired track for it to work. It is not a big problem and means that when correctly applied once back on track the pilot does not have to remember what the error was all they have to do is turn by the SCA again but in the opposite direction.