There's a lot of cases where Puppet fails on something similar. Packages is probably the easiest example. Puppet won't remove all package not explicitly declared, nor will it remove files it created, if you remove the Puppet code for managing that file.

I'm fairly sure that the way to make Puppet do what you suggest is the same in Puppet and Ansible. The difference is that Puppet is smart enough to not actually remove you file during every run (I think). On the other hand, Ansible will normally not be configured to run every 30 minutes like Puppet, so it's much less of an issue.

Both tools are great but they work some what differently. How you think about using them is much the same though, you need to tell the computer what to do. In Puppet this is often talked about is if you describe the state, I suppose that's partly true, but in the end you have a series of actions the computer will need to take to achieve this state.