These are the possible direct-speech attribution formats in English composition and exposition, listed here in the order of usage frequency:
1. "I will eradicate illegal drugs in three to six months' time," President Duterte said. (This is the more common usage in Western and Philippine journalism. It's hardly used in lead sentences of news stories. Often, it is used as a detailed, direct-speech attribution to the speaker's statement paraphrased or summarized in the lead sentence.)
2. President Duterte said: "I will eradicate illegal drugs in three to six months' time." (This is rarely used in English-language journalism and literature except as an emphasis device. I came across only one novelist, if I recall correctly it was John Hershey in A Bell for Adano, who used it consistently in the form of paragraphed dialogue.)
3. President Duterte said, "I will eradicate illegal drugs in three to six months' time." (This is the least used among the three direct-attribution styles. Perhaps some profession or field use it in its reporting, but so rare it is that I won't venture to say which one does.)
The style of direct-attribution used by a publication is actually more a matter of convention. The rules are not set in stone, as you surmised. In fact, if you study the history of journalism, you will find that newspapers and periodicals as well as fiction over the centuries varied widely in their direct-attribution style, with others even opting altogether for indirect-speech attribution .
