It seems that there are a few issues here- a privacy issue, a working hours issue, and a bill issue.
First, there is no law stating that you have a right to keep your personal cell phone number private. However, if you are worried about inappropriate contact with one or more coworkers (for example, someone has made romantic advances to you that you are uncomfortable with, and you fear he or she may stalk you if given your phone number), then this is a separate issue of workplace safety and/or sexual harassment that you should bring up with your employer. In that case, your employer should work with you to modify the policy or monitor the situation closely. Any inappropriate contact should be addressed immediately.
If you routinely take calls after hours, and you are an employee paid by the hour, then the time spent taking these calls is generally compensable and you should be paid for it- unless it’s a really small amount of time (“de minimis”). Further, if you are required to be on call, you are frequently called, and there are restrictions on what you can and can’t do on call, then your employer may be required to pay you for the on-call time.
Finally, if you pay for your cell phone and using it for work requires you to spend money, you’re probably not entitled to reimbursement unless you’re employed in California. This could be different, though, if paying the extra charges on the cell phone means that you’re falling below minimum wage. Be aware that you can deduct the business expense on your personal income tax return.