In all my years, I have never used tongs or any other holding device for the charcoal, nor have any altar servers or priests I've known. Fingers only. Play a flame against the edge of the coal, drop it into the censer once it starts to fizz, then wait until it has sparked all over before adding the incense. A very experienced altar server once told me to place the incense pieces beside the coal (touching it, of course), rather than on top of it, so that the incense burns for longer. But putting the incense on top is still OK.
And keep the lid of the censer open! The little holes in the lid are too small to let the coal breathe if the lid is shut. The lid should be shut to snuff out the coal.