The delivery includes ear inserts in various sizes (probably made of silicone) and the small 'wing' functions as a 'clamp' in the auricle for additional stability....
Well, every pinna and every ear canal looks a bit different. for me, l and r are not even the same. unfortunately, I could never use standardised in-ear fits without pain or slipping out. Individually fitted and laboratory-made earpieces, soft or hard, with or without anti-allergenic coating, for about CHF 100-150/piece can be bought at the local hearing aid acoustician if necessary. Before buying the headphones, ask if they are suitable for an individual fitting. Consultation costs nothing. If necessary, call in advance.