Your inversion should be kept in the chords and it should playback the notes you have selected. The inversion number displayed in the builder at the bottom (section C) is simply an indication. When editing the chord manually and clicking apply we consider the chord as being in its original form (inversion 0).
This is a choice we made for clarity, this way if you have a value other than “0” in the inversion selector it means your notes won’t be the way you set them in the editor.
It could have been the other way around, but as you noticed it can then be hard when adding bass note to understand the intent of the user.
Some people could expect the inversion 1 of a Cmaj to always have a bass in “E” for example but others might expect the bass in C to stay the same and the upper triad to be inverted. This will be improved once Scaler indicates the bass note of a chord separately from the handling of the inversion.