The apostrophe must only be used here to indicate a possessive, never to form a plural
- Customer's - we are talking about one single customer and something that belongs to them:
the customer's hat, the customer's request, the customer's money.
- Customers' - we are talking about many customers and something that belongs to them:
the customers' hats, the customers' requests, and the customers' money.
Customer's is used if we are talking about one customer. For example:
The customer's invoice was printed yesterday. (There is one customer.)
Customers' is used if we are discussing the possession of more than one customer:
The customers' complaints were mainly focussed on the unfriendliness of the staff.
Several customers have complained.
You could check a grammar book if you want to learn more
Is it not "customer service", without the 's'? That's how it is down in Aus. The 's is used to denote ownership, it doesn't make grammatical sense to denote ownership without it.
If I had to explain why its "customer service" and not "customer's service", I would say it's because the customer does not own the service, it's the business, i.e. the Sale's customer service department.
If the customer did own something, then yes it needs 's, i.e. the customer's handbag was stolen; if it's more than one, the customers' handbags were stolen.