Hello Stefania - i just tested this on my public box - I get Access Denied - when pushing the reload button in my published app as my Qlik Sense instance is setup for anonymous access - so in order to get this to work in your environment - you most likely need to configure security rules in the QMC for those NON DEV / NON ADMIN user accounts to be able to run a reload. Let me see if I can continue to trouble shoot - unless someone has already got this to work on a published app. I'll be back. :-)
You can allow published apps to be reloaded and saved by adding a security rule on QMC. For example, following security rule allows any users to execute reload button on published apps in "Everyone" stream.
(((resource.resourcetype="App" and resource.stream.name="Everyone") or (resource.resourcetype="App.Object" and resource.app.stream.name="Everyone")))