To reproduce: Change the monitors positions in the settings panel and try out on both monitors. Please refer to the attached file.

Workaround:

Dim tbLocation = Point.Empty
Sub New()
    InitializeComponent()
    Me.RadTextBox1.Text = "Once uppon "
    Dim tbSpellChecker As TextBoxSpellChecker = Me.RadSpellChecker1.GetControlSpellChecker(GetType(RadTextBox))
    AddHandler tbSpellChecker.DropDownMenu.PopupOpening, AddressOf PopupOpening
    AddHandler Me.RadTextBox1.TextBoxElement.TextBoxItem.HostedControl.MouseDown, AddressOf RadTextBox1_MouseDown
End Sub

Private Sub PopupOpening(sender As Object, args As System.ComponentModel.CancelEventArgs)
    Dim e As RadPopupOpeningEventArgs = TryCast(args, RadPopupOpeningEventArgs)
    If e IsNot Nothing Then
        e.CustomLocation = tbLocation
    End If
End Sub

Private Sub RadTextBox1_MouseDown(sender As Object, e As MouseEventArgs)
    If e.Button = Windows.Forms.MouseButtons.Right Then
        tbLocation = Me.RadTextBox1.PointToScreen(e.Location)
    End If
End Sub