Disclosed herein are coupled polymer products comprising polymer with up to five polymer chains bonded to a functionalizing compound of either formula (II) or formula (III), wherein the polymer chains are comprised of conjugated diene-containing monomers optionally in combination with vinyl aromatic monomers and further include vinyl group-functionalized aminosilane compound of formula (I) bonded within the polymer chain. Also disclosed are processes for producing the coupled polymer products as well as a rubber composition containing the coupled polymer product and tire components comprising the rubber composition.