That fear is logical, since the process of counter-steering and leaning is unbalancing in nature.
However, you need to understand that the bike and yourself are not falling in, rather both are relocating to an angle of new and perfect balance (both are coming back from a "fall" into a more stable position).
The reason is that the circular movement into which we commit, makes the "gravity forces" point non-vertically down, but towards one side and down (making the bike and yourself "heavier").
Think of the source of gravity under you shifting towards outside the curve while you travel into that curve.
All we are doing is relocating the combined center of gravity "over" the line joining both tires' patches, so those "gravity forces" go through that line.
For a constant turn radius, whenever we input steering movements during a curve, we are basically counter-steering and forcing the bike out of the "leaned" balance described above (disturbing the balance).
Actually, that is the only way to come back to a vertical position (new balance state) once the circular trajectory ends and becomes linear.
Think of the source of gravity pulling you shifting towards directly under the bike while you travel into that straight line (or shifting towards the opposite side in the middle of a chicane).
Hope this helps