An installation tool assembly for advancing a fitting's swage ring onto a fitting's connector body while a conduit is received in the connector . body to mechanically and sealingly connect the fitting to the conduit includes a body defining at least two spaced apart piston chambers, a fixed jaw connected to the body and adapted to engage one of the connector body or the swage ring, and a movable jaw connected to the body and movable relative to the fixed jaw. The movable jaw is adapted to engage the other of the connector body or the swage ring. Pistons are disposed in the at least two spaced piston chambers. The pistons and the movable jaw are configured such that movement of the pistons in a first direction moves the movable jaw toward the fixed jaw thereby moving the swage ring axially onto the connector body to mechanically and sealingly connect the connector body to the conduit received therein when the fixed and movable jaws are engaged to the connector body and swage ring. A crossover assembly follows the contours of the body and fluidly connects the at least two spaced apart piston chambers. The crossover assembly is fluidly connectable to a hydraulic pressure source for delivering hydraulic fluid to the at least two spaced apart piston chambers to move the pistons in the first direction.