д' sounds a bit like з to me
to me it sounds like дьзь. That can be his individual way of pronunciation, but it can be the result of exagerated separate pronunciation.
most of the soft letters are pronounced by touching the tongue to the lower teeth and saying the letter less emphatically?
Touching lower teeth is not obligatory, but it often happens because the middle part of the toungue is rased towards the hard palatum (which is behind the alveolars. I would say that soft consonants are tenser and more audible.