Yes, in many themes, fees added by Magical Fees can appear in cart progress bars (like free shipping thresholds). This happens because most themes calculate progress based on everything in the cart, including fee line items.
Magical Fees does not have any native integration with progress bars and cannot change how they calculate values.
What you can do
If you want the progress bar to exclude fees, the next step is to contact your theme developer. They may be able to adjust how the progress bar logic calculates cart totals.