How does the ULAT deal with teaching cultural issues?
It doesn't. The ULAT is not a program or textbook designed to teach about a single country or group of nations where a particular language is spoken. It is constructed to convey a foundational knowledge of the fundamentals of a language in the right manner, without any initial recourse to text or to the learner's native language.
One's knowledge of culture is best acquired on site. The acquisition of the tool (language) that allows students to experience the target culture first-hand is by far more important than providing them with second-hand bits of information. Of course, the ULAT's Language Pals sessions can also convey much about the culture(s) of the language's native speakers. The ULAT is a tool for developing language skills. Its goal is to put the learner in a position to be able to function in the target culture(s) as rapidly and effectively as possible so that he or she might then become immersed in the culture, which is the richest way in which to come to know it.