In cases like those, individuals from the less-developed civilization could integrate into the intellectual circles of the more-developed one, but the civilization as a whole could only reach that level, at great cost, if it made a deliberate, concerted, and holistic, effort to modernize. Typically it'd take a minimum of a generation before the tremendous costs started to pay off, with the advancement achievable only by importing experts from the rival civilization, and even then the sustainability of the progress can be called into question. Obviously during this time the senior civilization is capable of putting the kibosh on things if it so chooses.
The prerequisites for understanding a given technological artifact are the same as those for inventing it: you must first understand, recursively, all the technology it depends on for its creation and use.