I am directly facing the customer with direct eye contact and greet them... something which is common standard in customer service in retail. The customer unexpectedly and abruptly responds with "excuse me"... before then stating their order.

Can you not see me looking at you with my undivided attention? Can you not hear me greet you?
I'm all for an "excuse me" if I am not directly facing them at that moment in time, it is a reasonable way to get my attention, so I can serve the customer. 
In this particular case however, not only was I directly facing the customer and verbally greeted them warmly, I also got full eye contact from them. It wasn't as if they were distracted looking at the menu and wasn't sure if I was there to take their order.

Just a bit bizarre to disregard the welcome. Customer wasn't overly rude thereafter, customer happy with their drinks.