so that the actual amount the Blackhawks paid him exceeded his AAV. In other words, you can't sign a 10 year $50 million contract with $5 million AAV but actually pay him $9 million in years 1-5 and then he just retires after year five, so you've avoided the cap hit for a $9 million player for five years. They would have to pay a recapture penalty of the amount they paid over AAV upon his retirement. The team that actually received the benefit of the lower cap hit than dollars paid is the team that is hit with recapture.
If the amount the Oilers are contractually obligated to pay him is less than the AAV that applies to their cap, they could get relief of the difference.
That's they way I understand it at least.
Here's a table of the Shea Weber contract that gives some numbers to how it works, though it's pretty complicated to track.