Is the autonomic nervous system only activated by internal stimuli?
Short answer
External stimuli can drive autonomic responses.

Background
The autonomic nervous system is a visceral sensory and motor system. The viscera are the internal organs. Virtually all visceral reflexes are mediated by local circuits in the brain stem or spinal cord (Fig. 1). It is one of two major subdivisions of the nervous system; the other being the somatic (or voluntary) nervous system. The main distinction between the two is that the latter is involved in voluntary and conscious actions (e.g., movement, perception and cognition), while the autonomic nervous system is engaged in involuntary processes, such as regulating heart rate, breathing and bowel function (Fig. 1). 


Fig. 1. Autonomic nervous system. Source: Austin Community College  

Although by far most stimuli driving autonomous responses come from within (think muscle movements driving bowel movements, increased heart rates during physical exercise), outside stimuli do directly impinge on the autonomous system. 

For example, the cilliary muscle in the iris is under the control of light coming into the retina. The pupillary light reflex test is based on this principle, and is routinely used to diagnose damage to the visual system. Also, production of saliva is controlled by external stimuli (smell and taste of food and see the striking example below from @anongoodnurse). And technically, the entire digestive tract can be considered to be outside the body, as it is continuous with the skin and lining of the mouth. Hence, the mechanical stimuli impinging on the intestines by a moving bolus of food that drives the waves of peristaltic movements can, arguably, be considered to be caused by external stimuli too. Lastly, the fight-flight-fright response involving the hypothalamic-pituitary-adrenal gland (HPA) axis is often initiated by external stimuli (loud sudden noises etc.).

The most important characteristic of the autonomic nervous system, as said, is that the autonomous responses are not voluntarily controlled. While you can decide to look or track a visual stimulus, you cannot decide to move the bolus of food back up to your stomach, or voluntarily constrict your pupil. The way the input is received may not be the best way to distinguish it from the voluntary nervous system.

Didactic answer
If you are left with questions, the first place to go to is your professor.

Reference
- Kandel et al. Principles of Neural Science 4th ed. (2000). Ch.49 The autonomic nervous system and hypothalamus. p.960-81