Your employer's practice of correcting employee's hours is definitely illegal.
Under California Labor Code sections 227 and 1174, all employers are required to maintain accurate records of each employee’s hours of work and meal breaks each workday for a period of at least three years. In addition, employers are required to provide to each employee accurate, periodic wage payments in writing. By failing to accurately record all hours worked, your employer violates both provisions of Labor Code.
Most importantly, such unlawful practice likely harms its employees financially, because they are not paid for all hours worked. If you are a nonexempt employee (I assume you are), your employer must pay you for all the hours (and minutes) you worked. If your manager corrects your time cards or your clock-in or clock-out records without including your "off-the-clock" hours in your paycheck, your employer violates the minimum wage law, as well as other provisions of Labor Code. Under California labor law, employers must pay for all job duties that are “integral and indispensable part of the principle activities” for which employees are employed.
The agreement that your employer asked to sign is likely illegal and no California court will enforce it, because it violates Labor Code.
I recommend that you start recording all your hours on a daily basis. If you wish to pursue a legal action against your employer, I suggest that you talk to an employment law attorney who specializes in wage-and-hour claims
In alternative, you can file a complaint with the Labor Commissioner who will investigate the alleged violations on your behalf and recovery any backpay owed to you .
Either way, you will be a protected worker, and it is illegal for your employer to fire you for enforcing your rights.
I wish you good luck.
An employer may not change your time, PERIOD. You must be paid for all time you work, includign overtime if eligible and entitled. Of course, if you work hours contrary to the instructions of your employer, while they have to pay you for the hours worked they can take action against you for violating policy up to and including termination. However, if the employer is forcing or encouraging you to come in early or stay late but not document the time properly, then that is a wilfull violation of the Fair Labor Standards Act, a federal law, and perhaps state laws in your jurisdiction. You should discuss with an employment lawyer in your area as you may have various legal claims.
You are entitled to be paid for the hours that you work. It is not legal for your employer to alter your time card. He can have a policy that forbids you from working overtime and can discipline for you doing that. However, he still must pay you for the time you work.