Probably because if your songs were downloaded to your device, removing them from Samsung Music, removes them from your phone and, thus, removing it from Spotify. Spotify, like Samsung Music can only play your songs if they exist on your device, as opposed to a Spotify cloud playlist. Check to see if they are still on your device by going to the my files app, locating the music folder and looking for your songs. I do not believe there is a way in Samsung Music player to hide a song while still allowing it to exist on the device to be played by another player.
You need to understand that both Samsung Music Player and Spotify Music Player are just shells that find your songs on your phone and plays them. Having them appear in both players does not make them duplicate files, so they are not taking up any extra room on your phone. Very much like the Gallery is a shell for photos, the photos are downloaded to your phone's DCIM folder and then you can use any photo viewing app you want to view them or edit them.
