Be sure that you are in the "Songwriting" mode of the app.
Swipe up the sheet at the bottom of the screen and tap on the icon highlighted below.
If you don't see it, you must scroll the list of icons horizontally.
The chords of your song won't change as the app will switch to the appropriate parallel mode.
Example: If you are in "C natural major (Ionian)" and change to the mode to natural minor (Aeolian), the new "root" of your song will be "Am". This is the parallel mode of "C Ionian". The tones which these two modes exist of are exactly the same, but now "Am" is the new root note/chord
The mode is bound to your song. If you switch the mode in the "Modes" mode of the app, the mode will be switched back to the mode of the song if you navigate back to the "Songwriting" mode.