Many churches have policies stating that nonexempt workers are prohibited from off-the-clock work, such as answering calls, texts, and emails from home. But I'm looking for guidance in the circumstance where it is expected, and even required, for employees to answer such communications after hours.
Employers may require nonexempt employees to be on call at all times, but they must pay nonexempt employees their regular hourly rate plus overtime for all on-call time. For this reason, many employers explicitly prohibit employees from responding to texts, emails, and calls after scheduled work time.
Some states require employers to pay a minimum amount of time—usually two to three hours' worth—whenever nonexempt employees respond to an after-hours call, email, or text. If these employees are not on call and the church does not require an employee to respond to after-hours calls, texts, and emails, federal law still requires the employer to compensate the employee at least one-tenth of an hour of pay each time the employee responds to a call, email, or text.
In other words, your church needs to manage its expectations and costs. If it doesn't want this kind of activity going on, it needs a policy prohibiting after-hours communications, and it needs to communicate that policy regularly and directly. And then it needs its church leadership, including pastoral staff, to reinforce the policy, especially when it comes to the expectations of support staff. When a pastor refused to stop contacting his support person after hours with an expectation of an immediate reply, his church started deducting $100 from his pay for each text and email sent after hours. It didn't take long for the pastor to stop contacting his support person after work.
For a helpful factsheet on rules and violations related to overtime pay for nonexempt employees, see Fact Sheet #53 at DOL.gov. While this fact sheet explores violations related to the health care industry, the information also applies to churches.