Unless the customer tripped over the employee or something the employee had placed on the floor, they should be in the clear. The employee would have had to carelessly & recklessly do something to be liable.
I don’t have all the legal terminology & I am not an attorney.
The employee was acting as an agent of the employer, not necessarily the ASM. That means the employer is responsible, then the ASM, & then the employee (maybe).
As a rule the employee does not have many resources so the injured person will get nothing by suing them. Which is why the employer & the management is named in the suit. They have the "deep pockets" or the money. The store should have a liability insurance policy for just those incidents.
Now we can look at the injured customer. Were they exercising reasonable caution as an average person would or was the customer reckless, stupid or really clumsy? This would be contributory negligence on the injured person’s part & they would have to cover part of the cost of their own injury.
Without knowing more details & how the liability laws of the state, I can’t be any more specific.
It may be best to see an attorney, specializing in labor law & tort law.
It may also be a good idea to ask this attorney about ’wrongful discharge’ as far as the job loss. It may not be legal.
Good luck.