In my practice (square rule), I place tenons at a consistent distance from the reference edge, such as 2 inches from the edge with a 2 inch tenon. I try to have the mortises in line on the receiving timber in order to maintain strength and continuous grain. Others may have a centerline layout where tenons and mortises are on the centerlines of their respective timbers. As a practical matter, many different nuances of layout are employed to reduce interference of joints ie, half height tenons and free tenons to keep as much continuous grain as possible and avoid adjacent offset tenons. But I am unsure what you mean by offset tenons, I think the sense of the term is vague and can be taken in a number of fashions. Different framing systems have a different sense of regularity.

!/3 width is not common in tradition, I have seen 2 inch tenons common in 8 and 10 inch timber in local barn building.