I think as a western disciple you really shouldn't worry about this traditions too much. As long as you don't have an intimate teacher-disciple-relationship with a teacher, or don't have MUCH trust in him, there is no need to ask someone for permission to do something in your spiritual life. And hey, it is YOUR development! If this brings you any further, why should you not do it? I would advise you to not let such issues confuse you. What is important all about these things is the question, whether someone is able to help you move on with your personal and spiritual development and not which tradition such a person belongs to.
Anyway, if you are used to Kagyu teachings, you may have to adapt to a different use of terms and language and maybe even different attitudes concerning spiritual matters - but for the latter, I think, that depends more on the persons who run a particular center than just on the tradition.
And of course you MIGHT face sectarian attitudes in centers, which might be a topic if you mention that you have a background with a "different" tradition - but I would say that sectarianism might be a reason to not attend to such a center at all, as such a behaviour, or confirming such a behaviour in interested persons, does not reflect high spiritual development