May be a subtle difference.
Someone gives you a reason for something, and to make the statement conclusive, might add "… so there you go!" (Meaning "that's all the reason you need, now you can carry on").
"Can I have an apple please?"
"Yes, here you go!"
"Here you are", "There you are", "Here you go" and "There you go" are all used as pleasantries when giving somebody something that they have asked for. "So there you go/so there you are" are the variants which tend to have the connotation shown in Example 1, which can be slightly dismissive and is used when telling someone that you've told them all they need to know and there need not be further argument. (That is, satisfaction or vindication).
The definition you quote covers both uses, but "here you go/here you are" are only used in sense 'a', they are not expressions of satisfaction or vindication.