Does the American tax year run from Jan-Dec for employees?

Yes. Starts Jan 1st and runs to midnight Dec 31st.

Employees CAN use a fiscal tax year, say 1 June to 31 May, but it has to be proposed to the IRS and approved BEFORE the fiscal tax year begins.

Most people and most companies do not bother, even though there ARE advantages to have a different tax year than everyone else.