When you click the tags listed for a question, it takes you to that tags questions page, not that tags unanswered questions page. If you're seeing all questions with bounties, then the last time you had been on any questions page, you must have selected "featured" to view questions with a bounty. The system stores your last selection and presents that the next time as the default.
Steps to reproduce:
- for a question listed, select a tag for that question not the tags listed on the right hand side
- You should see the selected tags, featured tab, listing all questions with a bounty
To answer "is it a bug or is it designed like that?" I believe it was definitely designed that way. I suspect there is a partial form that handles displaying question previews. While I'm certain the behavior could be changed, I'm not sure it would be worth the effort.