"Fills" is sung to a dotted half note that takes up the entire measure. Musically, then, there's a representation of that "fill[ing]."
In looking over the hymn again in order to write this post, I also discovered a merism in the second verse: "By morning glow or evening shade / His eye is never sleeping." A merism is a rhetorical device in which two ends of a range are named as a way to refer to the entirety, so here, while "morning" and "evening" are what are mentioned specifically, the idea includes all of the time between them too.
