What you are seeing is probably the correct behavior even though it’s not what you want. If you look closely the arc is actually extended by arc to the point where it is offset normally from the original, but then further extended by line to reach the offset vertical lines. Perhaps an arbitrary choice, but probably also the most frequently desired.
The fix, as you’ve probably discovered, is to explode the offset curve if necessary, delete the straight extension and extend the arc manually “by arc” to the vertical lines and then trim off the extra part of the straight line. Rejoin if desired.
Would it be handy to have an offset command option to “extend arcs by arc”? Sure. Especially if your object had a lot of arcs and you wanted them all extended by arc.