How would you apply the major -> minor key change if there are accidentals?

On this forum, I have found a way how to change the key without changing the notes (so the pitches do change) - https://musescore.org/en/node/47336

(I recommend it if you are annoyed by the unswitchability of "Keep score (e.g. Maestro) x Keep pitches (MuseScore)".)

But how would it go if there are accidentals present? If it's the 7th note raised (harmonic minor scale), then the transition goes like "+2 sharps/-2 flats" instead of "+3 sharps/-3 flats". An example can be found here: (upload 2)

If I am trying to change the score from A minor = C Major to D major, it means I am just trying to add 2 sharps without changing the rest of the score.

That means I will - according to the linked guide - add the signature, then manually push all notes 2 semitones up (C -> C# -> D), and because D -> C is a second, I choose the "Diatonic Transposition -> Second -> Down". That should undo the manual push change, but also remove the accidentals which were caused by adding my key signature.

(Try that on C major scale and change the key signature to D major while removing all accidentals in the score, it will be c# - d - e - f# - g - a - b - c)

However, if you apply that on my score, you will get: (upload 1)

As you can see, the D flat (in the first line) changed to D natural. Is that intended? My change added an extra semitone to all C (and also F) notes, which also means that the D flat = C sharp got changed to C double sharp = D natural.

Now this was a technical question, but if you are interested in these, I'm gonna add theory question:
I applied these techniques on other scores of mine, which sound pretty good, but I probably misidentified a key (I have them written without key sig because of various accidentals) - because adding 3 flats or 3 sharps causes a mess in the music (usually an unison where it definitely shouldn't be is probably the most obvious). That means, is there a generic way to change a key in scores like these?