Due to conservation of energy, the sum of the energy due to velocity and the energy stored as pressure remains fixed. Therefore as the velocity goes up the pressure of the air at the narrowest part of the nozzle becomes quite low, even lower than atmospheric pressure. This is the Bernoulli effect.
The paint sprayer suction tube has one end in the paint and the other penetrating the wall of the nozzle at this minimum pressure point. Atmospheric pressure forces the paint from the reservoir up through the suction tube where it spill out into the path of the high velocity air. The air carries the paint along with it out the front of the nozzle where it is deposited on the surface being painted. If the suction tube did not reach to the bottom of the paint reservoir it could not reach the last of the paint.