I'm at the ch 3 -4 of the first season, so rather unsure what scene you are mentioning. As for our style - traditional, I guess? You can google taegeuk Iljang for the first form of poomsae to see what we practiced.
P.S. just googled moo duk kwan taegeuk form 1 - still got iljang. Can you post a link to a video of what you practiced? Had me curious for what it worth.