Key Signature not properly translating scores imported with no key signature

I have a piece written in E flat major using MIDI samples in a DAW. The notation software in the DAW has interpreted notes of the scale in an unorthodox manner, so that the 3 flats of the E flat major scale have been interpreted as sharps of the lower notes:

E flat is written as D#; A flat is written as G#; and B flat is A#. They sound right when played back, but are written incorrectly.

The file was imported into Musescore without any key signature. When I applied the E flat major key signature to Musescore, all the sharps remained the same—the notes were not shifted a tone higher to be interpreted as flats. This surprised me.

My question is, how do I get Musescore to translate the notes into the proper key signature? How do I get it to turn my D sharps into E flats, G sharps into A flats, etc.?

(I did try and research this in the manual and online, but most search results are about transposing in Musescore, or simply how to add a key signature in Musescore, and I couldn’t find anything.)

Hope someone can assist...