First of all, to answer the question of how to refer to someone in person - it depends on where in East Asia you are. If I was talking to the Chinese President, Xi Jinping, for example, I would call him Mr. Xi (Xi Xiānshēng) if I were speaking formally, Xi Jinping if I were speaking informally.

In Japanese, on the other hand, honorifics are very widely used, and using names is often avoided all together with superiors. If a name is being used, it's generally the surname - the first name is very informal.

In Korean, titles are used when possible (Manager, President, etc), and full names are used otherwise, unless you're talking to someone your age or younger, or a close friend, in which case you can use their given name.

As to why, I don't think there's really a particular reason. Where the name is placed makes little difference - if the West suddenly started using those naming conventions, would anything be different? Smith John would communicate exactly the same thing as John Smith does now.

As you can see from this map, it's a little more complicated than that. For instance, contrary to the rest of Europe, Hungary puts the surname before the given name. People in the Indian subcontinent traditionally only had first names, with surnames only being introduced under the British (and even now, you get people such as Mayawati, the former Chief Minister of Uttar Pradesh, who are still only known by one name). This custom is also still prevalent in Indonesia (cf. Suharto).

And in Vietnam, other complications arise. For instance, a person called Joe Smith Bloggs in the West would be known as Bloggs Smith Joe in Vietnam, just like in China. However, unlike in China, that person would not be addressed as Mr. Bloggs, but as Mr. Joe.