We may separate karma (the person's mental habits) and non-karmic conditions (external phenomena, i.e. things perceived by the five senses). This still maintains the impossibility of direct mental influence.
As for explaining mind terma, I can ask the same question. Or, to turn it around, I may say that such thing is not possible. And to give it another turn, such teachings are based on insight into the nature of mind, so it is true that they are from Padmasambhava (or any chosen enlightened being), since, as we can see in guruyoga, the mind of the teacher and the student are ultimately the same.
I do not see why you insist so much on the impossibility of direct mental influence. I see this as dualistic thinking. In my opinion, direct mental contact no more contradicts karma than a physical contact does. Both are made possible and effectual by the presence of appropriate karma on both sides.
Anyway, it is widely accepted that such things are possible. For example, Dilgo Khyentse Rinpoche:
Mind treasures arise in the following way: In many instances, after bestowing an empowerment or giving a teaching, Padmasambhava made the prayer, "In the future, may this treasure arise in the mind of such and such tertön." While doing so, he would focus his prayers and blessings on the tertön, usually an incarnation of one of his disciples. When, due to Guru Rinpoche's blessings, the times comes, both the words and the meaning of the treasure arise clearly in the tertön's mind. The tertön can then write these down without having to think.
It is also said in suttas regarding the powers of Buddha:
He knows the minds of other beings (parassa ceto-pariya-ñāṇa), of other persons, by penetrating them with his own mind.
which implies a direct mental contact.