Okay so going back and rereading some Fairy Tail chapters it came to my conclusion that Second origin still seems greatly confusing.
This is the explanation given by Ultear:
So my interpretation is that it improved upon the first container to allow you to use the second container. We all know Ultear magic speed or slows down time so my guess is that she speed up the progression of the first container which gave access to the second container of magic.
For Example: If certain characters Magical reserves were at:
Lucy: 70 Erza: 150 Natsu: 100 Gray: 80
If their first container was improved upon by lets say by a factor of 2:
Lucy: 140 Erza: 300 Natsu: 200 Gray: 160
with their Second container released:
Lucy: 280 Erza: 600 Natsu: 400 Gray: 320
This means their power increased by a factor of 4. This is just my interpretation of what SO did to their magical power. Although I personally think their magic power was increased by way more than a factor of 4 due to certain events. I also don't think they are using the rest of team Natsu is using their second container yet. I feel like they are just using their improved first container. Not saying that it's not released but I don't think they are fully using it.