If you were claiming that someone had made a mistake in their paper (in mathematics), then in that situation you should notify them beforehand and give them a chance to rebut your claim. (Keep in mind one of the possibilities would be that the claims in your paper are correct but you didn't understand the claims in their paper.) However, a refuted conjecture isn't a mistake, because a conjecture isn't a claim at all, only an informed guess (or, in some cases, a provocative way to ask a question). Hence, you aren't under some obligation to inform them before making the paper public. You certainly can if you want, and they could have some further information, for example further context for the conjecture, that would help you produce a better paper.
However, if you're asking about notifying them roughly simultaneously with putting it on the ArXiv, I don't see why you're asking. Mathematicians have a hard enough time getting anyone to read their papers as it is; by some measures of what it means to 'read', the median paper is probably read by fewer than one person not including authors and referees. The person who proposed this conjecture is naturally someone who is likely to be interested in your paper, and of course it is to your advantage if they know about it. If this is a well-connected senior mathematician who organizes conferences and workshops and might help you publicize your work further, even better. Without being obnoxious about it (and letting someone know that you have resolved their conjecture is definitely not obnoxious), you want to publicize your work to interested parties as much as possible.
Also, this person is a likely referee for your paper, and it will speed the process along if they happen to have already read your preprint prior to being asked to referee!