In Chrome, you're asked permissions when IndexedDB installs for the first time on a host (origin, port and protocol matching), but this is apparently not the default behavior in Firefox.
According to this helpful Mozilla support ticket, there seem to be two types of permissions in FF: "indexedDB" and "indexedDB-unlimited." Only the latter comes into play; the user doesn't have to grant permission until the 50mb ceiling is reached.
The ticket describes expected behavior as allowing IDB by default and not seeing a prompt:
Expected - app should finish loading and allow indexed DB by default
without a prompt
If you'd like to control permissioning consistently in a cross browser way, I suggest you take matters in your own hand as the spec does not proffer a way that browsers should be going about this and we can see Chrome and Mozilla teams already disagree.
For example, store a "1" in localStore
when the user grants permission and a "0" when she denies it. Refuse to open a database for someone with a "0" and prompt for permissions for those with an "undefined" as a flag.