Maybe your use of quotes is intentional here, but for posterity's sake there is no actual fine-tuning happening using user input in the code you linked, insofar as the weights of the model aren't being touched at all, nor are they modifying anything else that could impact the original weights (like a LoRA adapter). You touch on this, I think (?), in some of your subsequent language but it read as a little confusing to me at first glance. Or maybe I've been too deep in the ML weeds for too many years at this point.
The paper details the actual process, but the TL;DR is that the memory module they use, basically a draft model, does go through a pretraining phase using the redpajama dataset, and then an SFT phase with a different objective. This all happens before and irrespective of the inference-time task (i.e. asking questions about a given text). Also, as has been pointed out in other comments, the draft model could really be any model that supports long context and has decent retrieval performance. So the actual training phases here may be non-essential depending on your infra/cost constraints.