Even ignoring the rest of your logic - replies are different from mentions and can be inferred only by context of the tweet and not simply the presence of @disney in the tweet.

In your example, I would be Tweeting you explicitly saying “I’ll give you $5.” Maybe that’s a binding contract.

That’s not what Disney is doing. What Disney is doing would be like if I said “Anyone who Tweets at me owes me $5.” That’s obviously not a binding contract.

Disney is saying "in exchange for a chance to spread your message in our marketing materials, you agree to our follow our ToS".

You're really twisting words here. No that is not what is happening. I never agreed to any exchange. I should be able to tweet at Disney with that hashtag and not agree to their ToS. Nothing about a hashtag implies consent. It is not their service to set terms for. I already agreed to the twitter ToS. I shouldn't have to be worried about accidentally agreeing to terms just because I used the right combination of hashtag and twitter user.