I use DICOR 501LSW self leveling sealant on my TPO (thermoplastic olefin) roof.
From my Owners Manual: "Do not use silicone sealants". My roof had a cut similar to yours. I squeezed sealant under the covering, pressed the tear down, and placed more sealant on top. No problem.
From my Owner's Manual: "For Normal cleaning, standard household detergents or cleansers may be used." I use Murphy Oil Soap. "The roof requires special adhesives and materials. Do not use silicone sealants. " I use DICOR 501 LSW self-leveling lap sealant. TPO is thermoplastic olefin.