What you are not understanding is that there is only one of each content controls in the document i.e. Item(1), no matter how many tables there are, and they are not where you might suspect. This can easily be demonstrated with your test document and the following Word macro
Sub Macro1()
Dim oCC As ContentControl
    Set oCC = ActiveDocument.SelectContentControlsByTitle("ValueA").Item(1)
    oCC.Range.Font.ColorIndex = wdRed
    Set oCC = ActiveDocument.SelectContentControlsByTitle("ValueB").Item(1)
    oCC.Range.Font.ColorIndex = wdRed
    Set oCC = ActiveDocument.SelectContentControlsByTitle("ValueC").Item(1)
    oCC.Range.Font.ColorIndex = wdRed
    Set oCC = ActiveDocument.SelectContentControlsByTitle("ValueD").Item(1)
    oCC.Range.Font.ColorIndex = wdRed
End Sub
You therefore need a different approach e.g.

Sub getWordFormData()Dim wdApp As Object, myDoc As Object, oCC As Object
Dim myFolder As String, strFile As String
Dim i As Long, j As Long


    myFolder = "D:\"


    If Len(Dir(myFolder)) = 0 Then
        MsgBox myFolder & vbCrLf & "Not Found", vbInformation, "Cancelled - getWordFormData"
        Exit Sub
    End If


    Application.ScreenUpdating = False
    Set wdApp = CreateObject("Word.Application")


    With ActiveSheet
        .Cells.Clear
        With .Range("A1:D1")
            .value = Array("ValueA", "ValueB", "ValueC", "ValueD")
            .Font.Bold = True
        End With
        strFile = Dir(myFolder & "testfile.docx", vbNormal) 'There will only be one testfile.docx in that folder?
        i = 0 'Change to 0
        While strFile <> ""
            i = i + 1
            Set myDoc = wdApp.Documents.Open(FileName:=myFolder & "\" & strFile, ReadOnly:=True, AddToRecentFiles:=False, Visible:=False)
            For j = 1 To myDoc.Tables.Count 'Loop throughout the tables
                For Each oCC In myDoc.Tables(j).Range.ContentControls 'loop through the content controls in the table
                    Select Case oCC.Title
                        Case Is = "ValueA"
                            .Cells(i + j, 1).value = oCC.Range.Text
                        Case Is = "ValueB"
                            .Cells(i + j, 2).value = oCC.Range.Text
                        Case Is = "ValueC"
                            .Cells(i + j, 3).value = oCC.Range.Text
                        Case Is = "ValueD"
                            .Cells(i + j, 4).value = oCC.Range.Text
                    End Select
                Next oCC
            Next j
            myDoc.Close SaveChanges:=False
            strFile = Dir()
        Wend
        wdApp.Quit
        Application.ScreenUpdating = True
    End With
    Set myDoc = Nothing
    Set oCC = Nothing
    Set wdApp = Nothing
End Sub