There are several factors at play.
In the second example customer is singular. So you have to refer either to a customer or the customer. You can't say: Customer is always right.
Also, the customer is used to mean customers in general, not any specific customer or group of customers. We do the same with descriptions such as the consumer and the tax payer to refer to all people who consume/pay taxes.
But in the first example customers is plural. Here it is possible to speak either of the customers or just customers.
Customers, without the article, refers to customers in general, any customers, all customers - and not any specific group of customers.
We would use the same construction - without the article - if we were talking of visitors or football fans.
Visitors are asked not to litter.
Tax payers are up in arms.
On the other hand, to speak of the customers is to refer to specific customers, who have been mentioned earlier. This description implies a smaller, defined group, which is not the intention of the author.