When the Spitter spits on Nedry the spit hits the eyes and forehead and shirt collar and lower neck. When he turns the spit is all over his face. It wasn't runny enough to drip down his face like that, it was almost like tar when he touched it.
When it spits the first time and hits his chest/neck, he touches the spit to see what it is. When it spits again and hits his face, he puts his hands up to his face, spreading the stuff all over the place.