it's old question, i just read this.. so i will try to answer.
TADI: last or happen in the pass. but the timing isn't too far. few hours or minutes before(for day, u can't use this. but use "kemarin"). example: tadi aku belajar bahasa indonesia=i was learning indonesian language ( learned few hours or few min before). or, aku tadi pergi ke perpustakaan=i was going to the library
BARU SAJA: just happen (but it's already happened). example: aku baru saja selesai makan= i had just finished eating. or, aku baru saja bertemu ibumu= i've just met your mother
BARUSAN: it's same with baru saja (shorten for baru saja)