But does it get well vs we'll correct?
I was curious so I just tried it out and it seems to from my limited testing (about 10 different sentences) for what that's worth.
It doesn't seem like a difficult problem to solve and it appears that the auto-correct uses the word immediately before or after to determine which it should be. Since one is a noun and the other is a contraction containing a verb, it's fairly easy to distinguish which is correct based on the next word or any words following it.
For example, if I type: Well wishing, it will leave it as well, as "We will wishing" doesn't make much sense in English. If I type Well wish, it changes Well to We'll as it sees a verb and assumes that I meant the future tense.
It seems to trip over dangling clauses, such as: Well, after the movie, go home. However, it might just be interpreting it as an imperative sentence, so I can't say for certain if this is a failure of the algorithm.
It does have problems if used in conjunction with a word that's both a verb and a noun. For example, both water and wound can be used as either a noun or a verb. So if I type "Well water" it won't change it, even if I type the sentence "Well water the plants." but again that could be considered an imperative sentence, though it would be more correct to write it as "Well, water the plants."
My guess is that it just checks the preceding or following word and if it can be sure, it will make the correct decision, otherwise it will just leave it. For the majority of cases it will probably make the correct choice, but there are some edge cases where the correct decision requires seeing more of the sentence before a decision could be made.