There's no mnemonic - it's a question of whether the French verb needs à. Envoyer and dire do - envoyer quelque chose à qqun and dire quelque chose à qqun, so your first two are wrong. The correct grammar is
Je leur ai envoyé...
Je leur ai dit...
But the causative doesn't take à unless there's also a direct object. So je leur ai fait comprendre la phrase but je les ai fait comprendre.