It tells me I have unopened chests from previous tour challenges but I can't find them. Where will..

In your inbox

There is more then the chest you earn from winning, you get others in the Quest task page (icon at top left of the Stage selection and above the video replay list page) you get a free chest every 4 hours to open. Another is if you are part of a team and was part of helping get the Team Chest during a "weekend session: you get that Shared Team chest but also a runner up chest if you placed in a high enough position (depending on the level of team chest obtained). The Message inbox will not tell or bring you to the chests aforementioned or even give you a message, its an app push notification only thing afaik. Also per the Quest, it will show a number for when a new task is ready to be accepted to start it or collected.