The synthesis of functionalized polyolefins through coordination–insertion polymerization is a highly challenging reaction. The ideal catalyst, in addition to showing a high productivity, has to be able to control the copolymer microstructure and, in particular, the way of the polar vinyl monomer incorporation. In this contribution, we modified the typical Brookhart’s catalyst by introducing in the fourth coordination site of palladium a hemilabile, potentially bidentate ligand, such as a thiophenimine (N–S). The obtained cationic Pd(II) complexes, [Pd(Me)(N–N)(N–S)][PF6], generated active catalysts for the ethylene/methyl acrylate (MA) copolymerization leading to the desired copolymer with a different incorporation of the polar monomer depending on both the reaction medium and the N–S ligand. Surprisingly enough, the produced copolymers have the inserted acrylate both at the end of the branches (T(MA)) and in the main chain (M(MA)) in a ratio M(MA)/T(MA) that goes from 9:91 to 45:55 moving from dichloromethane to trifluoroethanol (TFE) as a solvent for the catalysis and varying the N–S ligand. The catalytic behavior of the new complexes was compared to that of the parent compound [Pd(Me)(N–N)(MeCN)][PF6], highlighting the fact that when the copolymerization is carried out in trifluoroethanol, this complex is also able to produce the E/MA copolymer with MA inserted both in the main chain and at the end of the branches. Accurate NMR studies on the reactivity of the precatalyst [Pd(Me)(N–N)(MeCN)][PF6] with the two comonomers allowed us to discover that in the fluorinated solvent, the catalyst resting state is an open-chain intermediate having both the organic fragment, originated from the migratory insertion of MA into the Pd–Me bond, and the acetonitrile coordinated to palladium and not the six-membered palladacycle typically observed for the Pd-α-diimine catalysts. This discovery is also supported by both DFT calculations and in situ NMR studies carried out on [Pd(Me)(N–N)(N–S)][PF6] complexes that point out that N–S remains in the palladium coordination sphere during catalysis. The open-chain intermediate is responsible for the growth of the copolymer chain with the polar monomer inserted into the main chain.