While it is not a requirement of the Labour Relations Act (which pertains largely to unions and dispute resolution), and while you are a manager, you are still an employee of your employer and thus have to comply with the terms and conditions of your employment. Often this includes various "office policies" and such.

If it is a requirement and is not unreasonable, then you will have to complete the register. The reasonableness is debatable but depends on the circumstances. On the one hand, the employer is entitled to have your full attendance at the workplace, and measures taken to enforce this are not unusual. On the other hand, an employer should trust their staff and not place the employment relationship in jeopardy by using draconian methods.