This issue has been mentioned several times in this forum.
With Windows and Dorico you can only use fonts with 4 styles: regular, bold, italic, italic bold.
As soon as you use a font with more than these 4 styles (and Minion has a lot of styles!) there will be a missmatch and you can almost never know what will be used.
The solution is to choose the styles you use and group them in 4 styles under a a specific “Font Family Name” and take care that each of the style you use correspond to the four basic styles: regular, italic, bold, bold italic.
For example group these 4 styles:
Minion Pro Regular
Minion Pro Italic
Minion Pro Bold
Minion Pro Bold Italic
under the Font Family Name: DK Minion
Then these 4 styles:
Minion Pro Medium
Minion Pro Medium Italic
Minion Pro Semibold
Minion Pro Semibold Italic
under the Font Family Name: DK Minion Medium
When you then choose these fonts in Dorico you will be sure that after installing these font Dorico will choose exactly what you want.
Be aware that to achieve this you need a Font editor (like FontForge) to be able to internally rename the fonts.
I believe there is no other solution