Sitecore 8.2u1
Previously InsertLinkButton
values were populated with InsertLinkButtonRule
(rule item id: {CEDD4633-193B-4D79-8DCC-C49B3C8D0F53}
). Where TargetControl of this rule is InsertLinkButton
and Trigger click

Action ID is {D4BA15D6-263A-43E6-93DD-CE9E41C7D8E4}
and it still exists in Sitecore 8.2u2 (/sitecore/client/Business Component Library/version 1/Layouts/Renderings/Resources/Rule/Rules/Actions/MakeInternalLinkFromTreeView
)
So you can use it if you want. I am not sure how your custom field works.
Sitecore 8.2u2
Now there is no InsertLinkButtonRule
rule which would populate button values. Instead, values are filled in JS.
If you open the InsertLinkButton
button definition you will notice that click property (previously empty) now has following value in it:
javascript:app.insertInternalLinkResult()
So you need to find a JS file. When you open PageCode rendering you will notice a path to the JS file.

After you open this file with a text editor you can see that there is an additional function called insertInternalLinkResult
.
Code fragment:
var itemLink = _.template(template, {
displayText: htmlEncode(targetDisplayTextID.get("text")),
alternateText: htmlEncode(targetAltTextID.get("text")),
itemId: targetControlID.get("selectedItemId"),
queryString: htmlEncode(targetQueryID.get("text")),
target: targetWindowValue,
styleClass: htmlEncode(targetStyleID.get("text")),
path: path,
anchor: htmlEncode(anchor.get("text"))
});
return this.closeDialog(itemLink);
Hope it helps.
p.s.
I used Sitecore Rocks to analyse the dialog structure.