Yeah, the soul stress track appears to replace the sponsor. The example in the book allows you to absorb backlash with the soul stress track. It also says you can self-inflict the stress to deal with any associated magic costs. I would interpret that to mean that if you want to increase the power of a spell, you can absorb the stress of summoning power with the soul stress track as well.
In other words, its just an additional stress track for magic casting costs only. You can cast longer and/or bigger with this additional stress track. Using your soul track to pay for your casting in any way triggers the catch satisfying effect. The +1 bonuses apply to any magic cast in the specified themes whether using the soul track to fuel the spell or not.
EDIT: Maybe I missed it, but the part that isn't clear for me is whether you can split stress between the soul track and other tracks. I want to cast a spell that requires I take 4 mental stress, but my #4 mental stress box has already been filled. Can I take 3 mental and 1 soul?
Personally, I'd say yes.