Since I am lazy and try to refrain from making larger walls of text than I already am, I'll be throwing in a few more pictures.
The HarvesterThis is actually the less complicated of the two. Mining vessels usually automatically due their stuff, but to planets, not ships.
This is the huge part both for refueling and gathering resources. "Allow other ships to fetch resources" allows strike harvesters to get fuel from the refinery, which will prevent your ships from exploding due to running out of fuel. "Allow other ships to deposit resources" will allow the strike harvesters to deposit their ore, if they so wish to. The "Allow other ships to supply resources" may or may not be important. I'm inclined to believe that if a tanker wants to supply fuel or ammo, this options lets it, or not.
Next part is carrier settings, but I'm pretty sure that's obvious.
This is the automation. I'm pretty sure when you make the design, this will all be done for you. You can take off the fetch fuel/ammo automation orders if you want. I don't believe they will mess with anything.
Strike Asteroid HarvesterNow this was the more difficult of the two.
The first two parts are to prevent other ships from stealing your harvesters fuel and to prevent your harvesters from dumping ore on each other. Though I'm not sure if this will actually happen, but it doesn't hurt to be safe.
The important part here is to "Deposit resources on ships" and allow other ships to supply resources. Otherwise, your refinery won't give your strike craft fuel while their operating. You can uncheck deposit resources on planets if you feel so inclined, it won't matter unless you have a planet in the asteroid system(which isn't that bad of an alternative either, I tried it once, though I started getting pirate raids.
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You can mess around with docking. It doesn't matter much. Though if you want to eliminate a few potential headaches, have them dock only in ships, or don't let them auto dock. You can have them auto dock when the system is under attack, though you will be forced to manually launch them every time a scout flies by.
Last part. Only thing of note is to deposit ore when over 99%, instead of the usual 25%. Not sure if it actually did anything, but it doesn't hurt to change it.