When did “docile” come to mean “calm”?

Solution 1:

According to the generally accepted theory, docile entered the English language in the late 15th Century.

It came from the Latin docilis (via Italian or French), which means "easily taught" (from docere ("teach")).

However, in the 18th Century, it came to mean "obedient" and "submissive," and still does today.

https://www.dictionary.com/browse/docile?s=t

Solution 2:

In addition to Ricky's answer, it could be argued that the job of a waiter/server is to manage customers and their expectations. Docile customers who are obedient or submissive to the waiter's requests are much more manageable than disobedient customers.

In addition, thesaurus.com gives a number of antonyms for "docile" including:

uncooperative, stubborn, inflexible, unyielding

These are all unpleasant qualities in a customer, and the wording of the sentence implies that the customers were at least some of these things prior to the free drinks. Crucially, it’s implied rather than explicit, which is always more polite. Being rude about rude people is just asking for trouble.

---Edit---

Following on from some of the comments on the question above, I think the usage in the question's sample sentence can best be described as a metaphor. The use of the word "docile" is commonly used in relation to animals. Therefore, it is implying that the customers behaved like animals, but softening the blow by using a word that is associated with good animalistic qualities and that is mildly ambiguous as to whether it always applies to animals or not.