やってくる is part of the TE+KURU construct that has kind of become its own thing.
In its most basic form, it would have been "to do something for a period of time" to arrive at the present or to get where the speaker is. Eventually it came to mean "to turn up, come along, come around," as in "Tanaka-san with turn up/come along/come around after the meeting." 会議の後に田中さんがやってきます。
Most of the examples I'm finding seem to place やってくる in a sense that at least implies a process, where as 来る simply shows movement.
会議の後に田中さんがやってきます - Tanaka probably has to drop off materials or pick stuff up before (s)he can come. (S)He may need to show clients out or catch a ride back to the office and so on.
会議の後に田中さんが来ます - Tanaka-san will come after the meeting - it's just mentioning the movement toward the speaker without any implied action or process.
まもなく、新しい年がやってくる - some sort of process took place until the new year could come (the new year took its time)
あらゆる種類の人々が展覧会にやってきた - These people turned up (implied process)