This is really interesting. I suppose tiny url gets a kicked back from their ad network for this. I'm the creator of the URL shortener (T.LY) and a Link Unshortener tool. I spend most of my development time fighting bad actors. My goal is to have a legitimate competitor to bitly that people benefit from. We do not set any cookies on redirects but do use cookies for authentication for users.
T.LY: https://t.ly/
Link Unshortener: https://linkunshorten.com/