You are corrcect, if you set Type to Student then they should each have their own Wiki. I have been doing it this way for ages as a way of providing student feedback. I set type to student and group mode to no groups. This then ensures that the students cannot see each others entries.
However, as of 1.7, I have been getting exactly the same problem as you (see http://moodle.org/mod/forum/discuss.php?d=60250).