Sforno on Numbers 21:13/ספורנו על במדבר כ״א:י״ג

1מעבר ארנון...היוצא, in that region where the river Arnon borders the region where the desert starts.

2כי ארנון גבול מואב, the border between the Emorite and Moav is a joint border only at that point where the river separates the two nations. The area where the Israelites had entered the territory of the Emorite was not anywhere near its boundary with Moav.