Competitive adsorption kinetics of three diblock copolymers, a poly(dimethyl siloxane-(poly(ethylene oxide) and two polystyrene-poly(ethylene oxide), at a hydrophobic solid-oil-water interface are investigated, under a nonuniform distribution of the copolymer in the aqueous phase. When exposed to a variable concentration profile of the copolymer, the solid-oil-water interface evolves through a time-dependent shape reconformation of the captive oil drop, which, for the two copolymers, reveals some strong qualitative differences. While the poly(dimethyl siloxane)-poly(ethylene oxide) adsorption results in a monotonically or stepwise shrinking of the captive drop in the whole range of the kinetics, the two polystyrene compounds exhibit a autophobic-like transition (early spreading/late stage shrinking). Based on the similarity in the number fraction of ethylene oxide units in the poly(dimethyl siloxane)-poly-(ethylene oxide) and one of the polystyrene compounds, this adsorption induced wetting singularity is interpreted in terms of i) the competition between bulk retention and interface adsorption and, ii) the conformation and rearrangement barrier of the adsorbed segments, both driven by the polystyrene chain.