You'll both feel a deep sense of recognition from the very beginning of your relationship, but as your affair continues, you'll also both feel a growing sense of discomfort with each other. At some basic level, your bond won't progress as either of you wants or expects it to, and this will likely be due to the fact that you're both connecting more on the level of those deep-past memories that are buried in your subconscious minds than you are in the here and now. That sense of recognition comes from another life, after all, and it will be difficult to separate those distant-past impressions from genuine cues as to whom your partner is today.
Furthermore, you'll also feel distanced from your own feelings for your lover. It will feel for both of you as if you're just not connecting, as much as you wish that you were. For you, there will be some lack in your psychic connection with this person, which will create a real emotional divide between you. In order to bridge this gap, you'll have to accept the fact that you won't always be on the same page emotionally. You may simply have to adjust to each other's rhythms and be content with only occasionally feeling that sense of warm togetherness at the very same time.