Hybrid-tieback seal assemblies, interventionless setting assemblies, and associated methods of setting downhole components of the hybrid-tieback seal assemblies using such interventionless setting assemblies are disclosed. A hybrid-tieback seal assembly comprises one or more anchoring bodies, one or more packer seal assemblies, and one or more interventionless hydraulic setting systems. A method of setting downhole equipment comprises applying a pressure to a compensating volume and providing a working volume, wherein the working volume is separated from the compensating volume by one or more hydraulic control devices. A pressure is applied to the working volume in response to the pressure applied to the compensating volume. The pressure applied to the compensating volume is then reduced and the pressure applied to the working volume is captured by the hydraulic control devices. The captured pressure in the working volume is applied to set one or more of the anchoring bodies and packer seal assemblies.