Where did this come from? I've checked The Chicago Manual of Style and other authorities, and the standard still seems to apply.
When independent clauses are joined by conjunctions, including and, but, or, so, yet, or others, the conjunction is preceded by a comma. The comma does not follow the conjunction unless there’s an intervening phrase.
We locked the door, but the burglar was already inside.
The news shocked everyone in the room, and one man fainted.
Do we want to offer health care to all, or are we interested only in our own situation?
The car wouldn't start, so we took a taxi.
Timothy played the guitar and Betty sang.
Go to the grocery for some celery and pay with cash.
CORRECT. Madelyn charged full speed, meeting life head-on, but Sarah held back, testing the waters before jumping in. (A semicolon could be used instead of the comma before but.)
INCORRECT. Madelyn charged full speed but, Sarah held back.
In sentences with short, closely related independent clauses, the comma may be omitted.
Leonard went north and Henry went south. I ordered fish and he chose steak.
The conjunction but shows a stronger separation and frequently needs the comma. I ordered fish, but he chose steak.
A comma is not normally used between the parts of a compound predicate—that is, two or more verbs having the same subject, as distinct from two independent clauses—though it may occasionally be needed to avoid misreading or to indicate a pause.
He had accompanied Sanford and had volunteered to write the report.
Kelleher tried to see the mayor but was told he was out of town.
She recognized the man who entered the room, and gasped. (The comma shows that she gasped, not the man who entered.)