What is non-determinism in the browser?
It's random numbers, the system clock, data off the internet, and input events from the user.
What it sounds like is that Mozilla has come up with a debugging environment that bottles all that nondeterminism up into a neat little package so that it can replay a specific run of your program any time you want.
It probably varies slightly, due to the entangled nest of dependencies that is responsive HTML rendering...
If you have an ordered map of pointers (e.g. std::map<void*>), iterating over the map will not be deterministic because the pointers given by a (regular) allocator are not deterministic.