Frequency adverbs like "often", "rarely", "never" , etc. can technically come before or after, and sometimes split, the verb phrase. However, as you've been taught, the better of your two choices would be placing the adverb after the negative verb: "I don't often watch TV" (or better yet, "I don't watch TV very often").
If this was an affirmative statement, you would be just as likely to see the frequency adverb placed before or after the verb. Either of these phrases would be correct:
I often watch TV.
I watch TV often.
The basic rule you've been taught is a good one to follow, although it's by no means a hard-and-fast one. There are exceptions, but there's almost always a better way to restructure the sentence in those cases using a positive verb:
I rarely don't watch TV for a week (correct, but there are better ways
to say it).
I rarely go a week without watching TV. (adverb first + affirmative verb, a better choice)
I do not often go a week without watching TV. (adverb second + negative verb, also a better choice)
You can read more about frequency adverb placement here and here.