As with most religious or mythical imagery, the satsuma immortals are shown as images that convey good luck, fortune, peace of happiness. They are shown as figures of peace who are fun loving, meditative or at comfort with each other and the rest of the world. Possibly images that were supposed to reflect upon the owners of the satsumaware items.
(http://www.satsuma-pottery.com/japanese-immortals-on-satsuma-pottery)