Yes, you can require this of exempt employees. The matter of working specified hours was addressed in the preamble to the exemption regulations, which were revised in April of 2004.
The preamble is a discussion of the rules, and the Wage & Hour Division (WHD) offered the following: “We agree that employers, without affecting their employees’ exempt status … may require exempt employees to record and track their hours; may require exempt employees to work a specified schedule; and may implement across-the-board changes in schedule under certain circumstances.”
There is nothing wrong with expecting exempt employees to work a specified schedule (i.e., to arrive by a designated time, to remain at work until a designated time, and to work a specified number of hours per week). If exempt employees could set their own hours, employers would have a difficult time managing their business and ensuring the availability of staff.