There are really no rules in punctuation, only conventions. And conventions, by definition, vary between cultures and ages.
One perfect example of this variety is the use of a comma directly before grammatical conjunctions such as ‘but’ or ‘and’. English school education often outlaws the practice of placing a comma before such words. US education, however, tends to take the opposite position. (For example, US convention dictates that the word ‘and’ at the end of a list absolutely should be preceded by a comma, as in “red, white, and blue”, which strikes English people as odd.) We should remember too that many business people in modern Asia and Europe are primarily educated in American-English rather than English-English.
The conventions may be different on different sides of the Atlantic but it would be small-minded in a big world to suggest that either party is right or wrong.
Returning to the origins of punctuation provides us with a useful rule of thumb. The very first punctuation marks were introduced by the ancient Greek dramatists to tell actors when to pause and breathe when delivering speeches. On one basic level, therefore, the comma represents a pause. If what you are writing were to be read aloud, would you want the reader to pause at this point, for clarity or emphasis? For example, if you were talking about “going to dinner with Jack and Jill”, you would not ordinarily pause before the ‘and’, so a comma seems unnecessary in writing. But if you are “playing football with Jack, and Jill is going shopping”, a pause (represented by the comma) seems helpful to indicate that two separate events are taking place.
If in doubt, read aloud what you have just written, see where you naturally pause, and add commas appropriately.