What Athom says is an efficient way to deal with the whole harvest busyness, and also why you'd want gas giants with moons, so you can do the operation on a single engine.
However, if I read right, you wanted fleets to directly take away from the tanker, which is also possible after you made that "tanker" tick in the design window. You will get the "refuel from target fleet" option when you have other fleets clicking for interactions with your harvester fleet.
You can even save the whole fly-in + refuel + back and deposit at colony orders, which I like to do after I get a couple mining sites, since it makes this a simple two click routine.