A family of Microsoft relational database management systems designed for ease of use.
No I don't think you need to store the customer in your product table. The relationship between a customer and a product is through the order, not directly. Unless your orders only include one product at a time, then you also have a transactions table whihc is where the Product is recorded.
So a Customer creates an Order, the CustomerID becomes a FK in the Order table. The order contains multiple items so the OrderID is a FK in the OrderDetails (transaction) table. To get a list of products a customer has ordered, you would have to use 4 tables; Customer, Order, OrderDetails, Products. The Relationships would be:
Orders.CustomerID<->Customer.CustomerID
Orders.OrderID<->OrderDetails.OrderID
OrderDetails.ProductID<->Products.ProductID
So your Product table would not have a link directly to the Customer. In the Orders table the only Customer field you need is the CustomerID as the FK. Similarly, the ProductID would be a FK in the Orderdetails table.