Why the -u flag doesn't work for ps?

Why the -u flag doesn't work for ps?

I'm executing the following ps command:
root@dor-desktop:/home/dor# ps u -t "$(tty)" -u mysql
USER       PID %CPU %MEM    VSZ   RSS TTY      STAT START   TIME COMMAND
dor       2070  0.0  0.1  22436  5240 pts/0    Ss   20:29   0:00 bash
root      2411  0.0  0.0  56028  1916 pts/0    S    20:45   0:00 su
root      2419  0.0  0.0  19532  2276 pts/0    S    20:45   0:00 bash
root      2488  0.0  0.0   4108   668 pts/0    S    20:51   0:00 /bin/sh /usr/local/mysql/bin/mysqld_safe --skip-networking --skip-grant-tables --user=mysql --b
mysql     2607  0.0  0.4 146552 19024 pts/0    Sl   20:51   0:00 /usr/local/mysql/libexec/mysqld --basedir=/usr/local/mysql --datadir=/usr/local/mysql/var --use
root      2672  0.0  0.0  15268  1224 pts/0    R+   20:59   0:00 ps u -t /dev/pts/0 -u mysql
You can see that the command asks for processes who are associated with the current terminal and who's user is mysql. But I get both types of processes!
How can I separate? I want only the process who initiated by the user mysql.
I found the following command: ps -C mysqld, which gives me want I need, but I prefer to understand what's wrong with the first command.