Smaragd,
If you had the wrong hex code, PilotAware would naturally consider your transponder (and any associated ADSB transmissions) to be a threat. Regards the warnings you were getting for your own aircraft, is your transponder rigged for ADSB out? If so, it might transmit ADSB even when the transponder side is set to Standby. You would need to check the manual and/or consult your supplier.
Under normal circumstances, your transponder/ADSB signal will appear on the traffic screen as this holds all received signals - like a collection box, before sending only those selected by the software to the audio alerts and your Nav System.
A screen grab of your traffic screen would help by indicating the 'mode' for the signal, e.g. CSA-P = Mode C, Mode S, ADSB and P3i or whatever combination is being received from that contact.
Regards
Peter