The home group is a strange thing that is left over from before you could actually control the ants with pheromone markers. In the first demo of the game, all you could do was build and the ants were entirely autonomous. There were no groups and all workers would do jobs including building, digging, carrying eggs, and collecting food automatically; soldiers could only fight and would go toward the nearest enemy, wherever it was.
We then introduced 1 group marker just for soldiers as an experiment (and decreased their aggro range from encompassing the whole map, to just a few tiles), people really appreciated this control. After that, multiple groups appeared and we muddied the waters with regard to who can do what: we let workers fight, and we let soldiers collect food.
As soldiers could collect food, it started to feel like food shouldn't be universally visible to the ants, and so in the same way as we did for combat, we reduced food detection range to just a few tiles - you must now tell ants to go near food with the marker or they wont collect it.
The three other jobs that only worker ants can do: digging, building and egg carrying are still universally visible (wherever the job is, they will do it). This is controlled by a 'job manager' that calculates the most efficient distribution of jobs within the nest and then assigns them to workers accordingly; updating periodically and swapping jobs if necessary (see the travelling salesman problem). The job manager also checks if the worker is in a group, and has its pheromone marker placed down: if the marker is not near the job, the job manager won't assign it. This means if all of your workers are in a group, and that group marker is set in location A, and you dig in location B (far away), no one will come to dig.
If you put your workers in the nest group (or any group with its pheromone marker currently disabled) - the job manager will automatically tell them to take eggs to tiles in an efficient manner.
If you want your workers to prioritise taking eggs to a specific room, you can actually use the pheromone marker to send them to that room; the job manager will then only give them nearby jobs, and they will fill up that room first. Though, this would probably be a very specific scenario emerging possibly in a future build (say you had a small room of highly upgraded tiles, or specialist ants, and you wanted those replenished before any others).
The nice thing about this whole system is that as long as you tell the player to "keep some workers in the home group", even if they don't really understand the mechanisms behind everything, they can play the game fairly well and it feels quite intuitive. However, when someone wants to really figure out how to do something efficiently, they need all of this explained properly - and the above is going to be difficult to get across in a short tutorial. We will try though.