Indexical uncertainties arise in philosophical discussions about Boltzmann brains, multiverse scenarios, cloning thought experiments, and Doomsday arguments, and really any case where you consider an observer trying to use Bayesian reasoning to determine his or her reference class. Other key-words are "self-locating uncertainty", "anthropic self-selection", "self-sampling", and here and here are a couple wikipedia articles that touch on the subject. A typical example of how it leads to subjective randomness in a deterministic scenario:
Suppose you enroll in an experiment in which you are blindfolded, taken into a room, and cloned. The clone always ends up in a red room, the original in a blue room. After the cloning operation you are then asked to remove your blindfold. At this point you have "indexical uncertainty" about whether you are the clone or the original, and so you predict a 50% chance of being in a red or blue room. Indeed, if you repeat the experience many times, you will find yourself in a red or blue room with a purely random 50% probability.
Now there are many puzzles and questions and debates about all of this, but as far as I know there is little debate about the basic concept, that subjectively pure randomness can arise from purely deterministic cloning scenarios. And of course in the MWI the "clones" are just branches of a universal wave function.