"Forgive me. I feel it again... the call from light. Supreme Leader senses it. Show me again the power of the darkness, and I'll let nothing stand in our way. Show me, grandfather, and I will finish what you started."
As we know, Anakin Skywalker can manifest. We also know that Anakin is strong with the force. Wouldn't it follow then, that Anakin is well aware of his grandson and is capable of manifesting to him? Wouldn't that change the conversation's intent quite a bit if we considered that Kylo is 'actually' talking to Anakin as Darth Vader?
Think about this: one act of good in a life full of the evil that Darth Vader committed does not necessarily mean he would be turned to the light permanently would it? If he spent the majority of his life believing in the dark side, following it, using it, and not least of all practicing it in a way that causes massacres and enslavement, doesn't it make sense that he would return to that way of thinking? What if he is directing and coaching Kylo? What if he regrets that after an entire life devoted to something he turned on it and now wants to reclaim that side of himself?
I think it makes no sense whatsoever to have Kylo speaking to his grandfather and saying 'show me again' unless he has been having communication with Anakin.