A lot of the assets from the game are pretty old, so they don't naturally fit to characters (its annoying I know). You have three options, I'll explain them each (Option 3 is probably your best bet):
1) what you're doing in that image – Daz studio has a native autofit script, and if you just select "genesis 2 female" for "what figure was the item orignally designed for," then "hair" for "what type of item is it," it should fit to your figure's head.
There's a couple problems with this option. Autofit is not always the best, and it might mess up how the hair is placed on the figure's head, and it also messes up the hair's bones/nodes (These are the things that allow you to pose and move different parts of the hair independently). If you do this, you might notice Caroline's hair bend in a weird way, or not be able to be posed properly. By and large, I would suggest NOT doing this.
2) Download a script – You can probably buy a script that converts the hair to genesis 3 without messing up the bones. I know Riversoft Art sells scripts that allow you to convert genesis 3 characters and clothes to genesis 8 and vice versa, but I'm not sure about hair. Obviously, the main downside of this option is that you have to find it, buy it, and then learn how to run the script. This is better than option 1, but still not great
3) The most common and useful workaround is to load your hair into the scene without fitting it to any figure. All you have to do is make sure nothing in your scene is selected, then load the hair in. If you already loaded the hair into the scene, you can right click on the hair, select "fit to.." then select "none". Then make sure the figure is in 0 pose (i.e. the T-pose it comes loaded in as). Then move the hair to the position on the figure that looks correct. Then parent the hair to the head. You can parent the hair to the head by going to the scene tab, then either dragging and dropping the hair on top of the "head" node, or by right clicking the hair and selecting "parent to" then scrolling to the head. This will make the hair move around with the rest of your figure's head when you pose the figure.
Let me know if that all makes sense. Again, I would suggest trying option 3
