When OnSong transposes a song, it uses the enharmonic preferences of the key you are viewing. For instance, then key of C# major is a "theoretical key" in that music theory prefers the enharmonic equivalent key of Db major so that you don't end up with weird things like E# or double sharps.
Now that said, one way to change things is to simply turn off transposition. To do this, open the Style Preferences Menu by tapping on the sliders icon in the Menubar. You can then choose the Chords tab and turn off the power icon to the right of the Key field. This will display the chords as you have then written.
Another way to handle this is to enable Theoretical Keys. With this enabled, you will be able to choose sharp major keys instead and have the enharmonic preference you prefer. To do this, open the Utilities Menu by tapping on the gear icon in the Menubar. You can then open Settings > Menu Settings > Style Preferences > Chords > Key. Here you can turn on the Theoretical Keys setting. Tap Done and go back into your Style Preferences Menu. You should now have three rows of keys instead of two with the bottom row allow for sharp theoretical keys.