This is going in circles. That rule does not apply in this case. Why? Revisit the two versions:
1. Winter finally is here.
2. Winter is finally here.
Again, I ask: Assuming that the rule applies here, why is it that that the first version must be set off by commas, but the second version doesn't? Yes, the "finally" in the first sentence is an interrupting modifier, but as I noted above, commas do not resolve the interruption. In fact, they obstruct the flow even more, if anything. The rule described by your two links generally does not apply to adverbs.
And as I said before, in MIT link, the author specifically wrote, "you can often get away with interrupting the structure of the sentence with a short (one-word) modifier." This is one of those situations.
I'm done here. If you wish, you may continue this on my profile, though I'm not sure how else to convince you.