Your understanding of since is correct.
Perhaps you might get confused with the sentence structure, and maybe also "which particular time" this "since" begins.
Let's look at the sentence. I will use parentheses to make it easier to understand,
(The US, Japan and South Korea) say (they have since defied the ruling).
I believe that you already know that the word "they" refers to "The US, Japan and South Korea".
Now let's analyze this clause:
(they) (have since defied) (the ruling).
The verb is "have defied". We also have the adverb "since" to indicate "since when they have defied the ruling". This implies that the reader should have already know this "when", usually from the previous sentences.
I found your news in BBC's website. Here are some sentences before the sentence you asked:
China says it scrambled fighter jets to monitor US and Japanese planes as they flew in its newly declared air defence zone in the East China Sea on Friday.
China said last week that all aircraft crossing through the zone must file flight plans and identify themselves or face "defensive emergency measures".
If I understand the news correctly, "the particular time" that our "since" starts from would refer to "last week", or more specifically the last "Friday".