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Unfortunately, the FSLA when written made no mention of vacation, so employers aren't bound by any laws about how they choose to utilize their vacation programs, if they even choose to have one (because they aren't required to).
For instance, it is illegal to subtract an hour from your pay check if you were to miss an hour of work one day, as a salaried employee. If you work at all that day, by law you get paid for the entire day. However, an employer can deduct that same hour from your vacation pool, as long as your check is the same rate that's all that matters in the law.
So, to that end, if the employer requires employees to keep up with their work emails in order to utilize the company leave program (which again, is not required in any state in the country), then that is legal.
You could argue for a prorated use of that vacation, rather than getting a full day credit for time worked on vacation, but that is a matter of your employer's vacation policy and how it can be interpreted. Further, you'd have to sue your employer in state court on your own. This isn't the sort of claim the Department of Labor would consider, because it is about contract issues and interpretation.