「引{ひ}く」 and 「惹{ひ}く」 are originally the same word "hiku". The verb "hiku" already had different meanings when Japanese was merely a spoken language. After learning the kanji from the Chinese and creating the kana on our own, we started writing some of our same original words differently according to the meanings that they are used for.
In the case of "hiku", we decided to use 「引く」 for physical "pulling" and 「惹く」 for psychological "attracting". The "connection" between the two should be clearly seen.
What makes your question this time unnecessarily tricky is that you have brought the new colloquial/slangy meaning of 「引く」 to the table. That meaning is "to get turned off", "to be put off", etc. 「ドン引{び}く」 is the emphatic form of 「引く」 only for that slang meaning.
If you are ドン引く-ing, you actually are pulling your body physically and/or pulling/drawing your mind back mentally from something. So, there still is the notion of "moving away from something" left in the new slang meaning.
If you compared the new meaning of 「引く」 to the original meaning of 「惹く」, however, the two meanings would seem quite opposite. Unless I misread your question, that is what you wanted to say.
The last thing I would like to mention is that it is nothing new that a word acquires a new colloquial/slang meaning that is very different from its "original" meaning.
Take 「適当{てきとう}」 vs. 「テキトー」, for instance. That is "appropriate" vs. "random". Pretty random, yeh?
「やばい」 vs. 「ヤバい」 for "chancy", "dubious", etc. vs. "great", "cool", etc.
This, however, is hardly a Japanese-only phenomena. Think of what happened meaning-wise to words such as "awesome", "bad", "sick", etc. If I have to learn the new meanings for those, you will have to learn the new meanings of the words I mentioned above.
