The phrase "it came right as" implies that one action (it) had just occurred at the same time another event is still taking place. It's a bit difficult to explain in the abstract, so let me provide a few examples of its usage:
Here's a rather simple one. If I say "The apple fell from the tree right as I was coming outside", this means that at the same point in time that I was coming outside, the apple had just fallen from the tree.
If I say "I had finished my homework right as the dog started barking", it means that at the same point in time that I had just finished my homework, the dog then started to bark.
In your example, the first action that was just completed is unspecified, probably given in an exterior context. The ongoing action is that "President Trump and the Japanese Minister were sitting down for dinner at the presiden's resort".