The same dynamic does not reproduce if the multifield is not nested in a tab.
This is, more or less, the situation before clicking on the button to move the fields:
(some of the fields are blanked out, but they are actually there)
And this is an image of what happens when you click on the highlighted icon to move the field up and down:
As you can see, the scrollbar disappears.
To be more specific, this line of code in the coralui3.js is executed:
Which sets the overflow property of the coral-panel-content (basically the container of the entire tab, that starts right under the Main title) to hidden (default is auto) :
We are on a 6.5 istance and, if it can be helpful, the content.xml of that dialog (which is just an example: the issue is present in all dialogs with multifields nested in tabs) is the following: