The crux is how you define the word "deviation." One can think of it as the difference between two angles, or as the ratio between two angles, or something else.
Recall Snell's law, perhaps rearranged, for two media with indices of refraction $n_1$ and $n_2$:
$$\sin \theta_2=\frac{n_1}{n_2}\sin\theta_1.$$ Here, we see that the outgoing angle from the normal, $\theta_2$, differs from the incoming angle from the normal, $\theta_1$, when $n_1\neq n_2$ and, as pointed out correctly, $\theta_1\neq 0$.
A more precise language says "that the sine of the light's incident angle gets multiplied by something other than $1$ in order to yield the sine of the light's outgoing angle is called refraction." This precise language still has the light's path "deviating" by some $n_1/n_2$, but only if we define the "path" as the sine of the angle $\sin \theta$ and the "deviation" as a multiplication instead of as a subtraction. Then, we can still say that the "path" is "deviating" but because the "path" is 0 and "deviating" means multiplying then the number doesn't change. Small consolation, you can alternately conclude that your professor was using language that is not 100% correct.
You can take the small-angle approximation, where $\sin x\approx x$, to see Snell's law for small angles as $\theta_2\approx \frac{n_1}{n_2}\theta_1$. Then this ratio $\frac{n_1}{n_2}$ is the same as the ratio between the two angles $\frac{\theta_2}{\theta_1}$, so the index of refraction is thereby the "deviation" between the two paths in terms of the ratio of the two paths' angles.
This sort of distinction is important everywhere. Say you take a test and you score "deviates" from your previous scores. You might talk about the deviation in terms of the difference between the scores and you might talk about it in terms of the ratio between the scores, where each will provide different insight. The same goes for an experiment with an expected and measured value. Often the ratio is more informative than the difference, often the ratio of the difference to the actual value is more informative, etc., and it all depends on your problem, but of course you should use precise language whenever possible.
In this case, it does make sense to talk about the path in terms of the sine of the angle, if you watch the light propagate and want to know how far it has propagated along the direction perpendicular to the normal. Whether or not you are happy to refer to the "deviation" as the multiplication of this value by something is up to you, because any time you define deviation in that sense you have to worry about the edge case where your value is $0$ and thereby unchanged by multiplication.
