You've almost got it right, but
remind has some odd behavior when you give a date spec that includes a weekday and a day. From the man page:
Note that when both weekday and day are specified, Remind chooses the first date on or after the specified day that also satisfies the weekday constraint. It does this by picking the first date on or after the specified day that is listed in the list of weekdays. Thus, a reminder like:
REM Mon Tue 28 Oct 1990 MSG Hi
would be issued only on Monday, 29 October, 1990. It would not be issued on Tuesday, 30 October, 1990, since the 29th is the first date to satisfy the weekday constraints.
You can get around it by adding
FROM to your command:
REM Tue Thu Fri FROM 13 Sep 2011 +1 UNTIL 28 Sep 2011 MSG Esem