The outside pass around the greens is called the "cleanup". We mow the cleanup pass around our greens with a walking mower and do this every other day. We skip days because this area of the green is usually where grass thins out. Every other day is an industry standard for most golf courses. Some times of the years it is very apparent on days that the cleanup is not mowed. Don't worry, it will get mowed the next morning and this will help keep the grass healthy on this high stress area.
The second photo is of a televised PGA Tour event. You can see the stops and starts of the greens mower and see that the clean up is either being mowed either every other day or with a mower with a slightly higher mowing height.