You don't need to chill the kegs(the cold cider will do that for you), but they should be pressurized prior to filling. The rig I use fills the keg via the spear, and has a ball lock valve attached to vent the headspace. By opening or closing the valve, one can control the speed of the flow since the pressurized keg and bright tank are in equilibrium.
What keg cleaning process are you using? All the ones I've seen/used pressurize the keg after the clean & rinse cycle.