By 'spitting' I am referring to the steady stream of water that is
ejected at the back of the motor when it is running. The motor is a
90hp Mercury 4-stroke. For this type of motor, when it is out of the
water, should water also be ejected somewhere else, such as the
through hub exhaust as you mentionned ?

If you are getting a steady stream through the tell tale then water must be
coming out of the hub.