Auto Fill Cell Value added by "Copy N Paste"

Try this:

Private Sub Worksheet_Change(ByVal Target As Range)
    Dim r As Range
    Dim cell As Range
    
    Set r = Intersect(Target, Columns("I"))
    If r Is Nothing Then Exit Sub
    
    Application.EnableEvents = False
    For Each cell In r
        Cells(cell.Row, "J") = Environ("username")
        Cells(cell.Row, "K") = Now
    Next cell
    Application.EnableEvents = True
End Sub