「てくる」can mean that someone goes somewhere and comes back with a direction verb such as:
マクドナルドに行ってくる。 I will go to McDonalds and come back
But it can also mean that someone did something before coming physically to where they currently are, although it sounds strange in English:
I ate (before coming here).
I saw it (before coming here).
Finally, that time came (and is here)
I came home (and am now here at home)
It can also mean that they have "come to" start doing something.
I came to understand.
I came to be able to speak English.
I believe in your example sentence, 聞こえてくるぞ describes how the person goes to work and hears about a certain topic of conversation all the time before, presumably, coming home.