I checked it with using your courses:
mysql> create table t(f text) expand_keywords='1' min_infix_len='3' index_exact_words='1';
mysql> insert into t (f) values ('тоби');
mysql> insert into t (f) values ('актобин');
mysql> select * from t where match('@f ^тоби$');
It returns both documents instead of a desired one.
How to search by exact string in this case?