Since I never automate workers I've never noticed this myself, but there could be a reason for farms outside the fat cross -- irrigation chain. If they need to irrigate to another tile inside the fat cross, but there are valuable improvements in the way, it would make sense to chain the irrigation around the other improvements. I'm not so sure they've been programmed with that level of foresight, though, considering how they will replace towns with farms, then cottage those same farms.
Other than working resources inside the cultural boundaries, there is only one reason to work a tile outside a fat cross. If you've got nothing else for your workers to do, building cottages/mines on the edges of your cultural boundaries will give invading units something to pillage, slowing them down before reaching your fat cross. I specify cottages and mines simply because they take less time to build than other improvements, such as farms, mills, etc. If you've noticed them building farms outside the fat cross, not on a food resource, then it is unlikely this is the reason, as it would be more time efficient to build cottages or mines.