My family had no problem bringing our "American-style" carry-ons on board in Danang (we'll see what happens later in TPE). It was funny because the lady working the gate made a beeline for us in the gate area just before boarding began. I thought she was going to hassle us about our bags. Nope. She just correctly guessed we were the Americans who had checked in online and wanted to do a doc check (apparently scanning the passports online was inadequate). She then let us board first.
I liked the airline. The only thing I'll do differently next time is try to check in at the 48 hour mark to try to get the best free seat assignments. They do let you pick your own seats at 48 hours.