I have a Magento store running 1.9.1.0, it appears that user sessions are being stored incorrectly, because:
If user logs out of their account: on the home page, it's fine, but then if they go to a product they've already visited, they're logged back in automatically.
I believe this to be related to caching, and disabling Fishpigs Bolt seems to fix the issue, but this hasn't occurred on other stores I have with Bolt
How can I ensure that Magento sessions are not cached in such a way?
Although it looks like the user is logged in, it's highly likely that they aren't logged in and that it appears that way because incorrect content has been cached. This shouldn't happen and with the latest version of Bolt, does not happen.
My first suggestion would be to upgrade Bolt to the latest version, which is currently 2.2.0.4. After doing this, fully refresh your cache and see whether this fixes the issue.
If this doesn't help, please contact me directly (I'm the creator of Bolt) using this form and I'll help resolve the issue. After that I'll edit this post with the correct solution.
UPDATE/SOLUTION
This issue was caused because of an incorrect Varnish/Turpentine configuration that stripped the 'frontend' cookie from Magento. As a result the FPC was unable to determine whether the user was logged in or had items in their basket. Removing Varnish/Turpentine resolved the problem.