I am a psychic medium and I use my natural gifts to aid in my spell work. As you said visualisation is a very important part of spell work, something most psychics are very good at. I believe that everyone on some level has psychic abilities, but like anything if you don't practice and develop you will be average at best.
In my opinion divination has a very solid place in witchcraft. I do think that the two work together.
I also understand quite well how my psychic/mediumship abilities work as do a lot of other psychic/mediums that I know. For example, when reading someone my information comes from linking my aura with theirs, if I was doing mediumship then I would link to spirit through that original psychic link. It is a conscious process, and while sometimes it does just happen (usually to let you know something important) most of the time it is intentional and requires focus.