Ink can hang out for awhile in carts. Either way works. Filling all the carts at once would certainly cut down on the amount of mess. Just do the priming right before you place the carts in the printer so you don’t have any ink that is drying in the outlet. Also make sure the carts are air-vent plugged when they are sitting and then remember to take the vent-plugs out before putting them in the printer.