Okay so first off if this a job you are thinking about taking just don't. Legal or not I have never had a job do anything like this or anything close. At the very best they are looking to screw you, at worst they are stealing.
As for if this is legal (nal) my understanding is that for no reason can a company in the US dock, fine or in any other way deny you wages for any work already performed. It doesn't matter if you did the work you need to be paid at the agreed rate. They can come up to you and just say that from this point forward the pay will be different, but only for future work.
The one exception to this that I am aware of is if you sign an agreement with them that lets them do this. Such as fines for lost uniforms. Often this will end up in a legal grey area though very few good businesses will do this.
TLDR business have to pay you for time worked. Crash the company truck they can fire you, but that last check has to be in full.
The vast majority of employment is not under contract. That is why employment can be severed by either party at any time. So an employer could change a wage on an employee but there is nothing saying the employee has to accept it.
No there is an employment agreement, but not a contract. So the employee and employer both agree to the terms of the work. This is just no requirement for the agreement to continue if either party wants to sever the agreement.