Yes, I guess those statements about error handling do imply the behavior I'm seeing. They don't immediately make me think of that behavior, though. I'll try to figure out of I can make it clearer and try a doc patch if so.
Since Try::Tiny says it exists to avoid the mistakes people make using eval for this kind of thing it does seem like using it again inside the the finally block as needed is what the authors had in mind...should be amusing.
(I only had one place in the code I'm actually working on where I'd messed up use of try blocks, but it was good to run through and check all the ones I'd added to be sure.)