The broad answer is that all federal government employees must get paid during a shutdown no matter what.
One of the main reasons for this is that unless specifically authorized by law, no one is allowed to volunteer for a federal agency. However, federal employees' paychecks for time worked during the shutdown may be delayed until the shutdown ends.
But if you are furloughed in a shutdown, as are EPA employees, it is a furlough without pay. After the shutdown ends, Congress may choose to pay those workers who were furloughed for the time they were out, but that's entirely up to them to decide.
Take a look at which types of federal employees get paid during a government shutdown.
President Barack Obama. The president has constitutional duties and so will remain on the job throughout the shutdown.
Members of Congress . Yes, lawmakers caused the shutdown, but like the president, they too have constitutional duties and will remain on the job while being paid on time throughout the shutdown.
Congressional staffers. Staffers who work during the shutdown won't be paid until after the shutdown ends and their bosses pass a funding bill.