When an on-call employee is required to stay at the workplace or is so near the workplace that he cannot use his time freely, he is engaged to wait (on duty). In such cases, the employee must be compensated for this time.
If an on-call employee must carry a paging device, such as a beeper or cellular phone, and the employee is relieved of his or her duties, the time is unpaid unless the employer has an on-call policy that specifically requires pay during such times.
Federal court decisions have held that on-call employees are not overly constrained by a paging device. Therefore, the unpaid, waiting to be engaged status could apply to those employees who are not required to wait near or at the work site.
As with any nonexempt employee, federal law requires that on-call nonexempt employees still must be compensated at or above the minimum wage and must be paid overtime for all hours worked in excess of 40 in any given workweek. Also, employers should make sure to check state laws on minimum wage and overtime.
So what does this mean? Basically, if you cannot freely enjoy your time off work, you are "engaged to wait" and are on duty and entitled to compensation.
If your employer does not want to pay you for this time, s/he should not require the 30-minute response time to calls and should not be requiring you to be in any particular proximity to the workplace during your time off work.