***Not a teacher***
Here is an example of its use, following a sentence with 'first' in narrative text.
"He began to search in the kitchen first, then a few minutes later, he moved into the dining room to search there."
I would call it a 'sequencing word' in the sense that it helps to provide an idea of sequence in a story (although I must admit, if 'sequencing word' is a recognised grammatical term, I am only guessing at its meaning).
Does this answer your question? Or are there other things about its use that make it seem complicated to you?