It implies that there have been 29 other reports before this one, which is the 30th one.
It might be used in a context like: The boss sent some people to photocopy a report, and they made 29 copies, but that wasn't quite enough, so the boss sent them back to the photocopier again and now "they are copying a thirtieth report".
It's a correct English construction, but not by any means common I don't think...! I'm a native speaker and I had to think to twice to understand it :)
I had to find a way to remind myself about the difference as well :) I dont know if it will help, but I always think "tretti" is "three tens" (3 x 10 = 30). "Tretten" (13) has a closer ending to the english word "thirteen".
From there is easier to rememember "TRETTENde" and "TRETTIende".