If the tutors are American, they will teach in American English, but when quoting British-English literature they will retain the grammar, vocabulary and spellings of the original quotation, i.e. British-English.

American textbooks on English Literature will instruct using American-English idioms and vocabulary.

English Literature textbooks published in the UK will use British-English idioms and vocabulary, grammar and spellings.

If you are neither American nor English, you may feel confused by the differences between these two forms of English. There are differences, but you will soon come to understand and appreciate both forms and realise that the differences are, in reality, relatively insignificant.

There are a few spelling and grammar differences, and rather more differences in the vocabulary and idioms used. Pronunciation will also be different, but even within countries regional accents vary among native speakers.

Studying/learning in either form should not be a problem.