Increment

So who is in charge of creating an increment during a sprint ?

No one is "in charge".  Just as I called out those words, let me call out specific words in the statements you quoted from the Scrum Guide. I will bold the words I am going to reference.

Developers are the people in the Scrum Team that are committed to creating any aspect of a usable Increment each Sprint

The entire Scrum Team is accountable for creating a valuable, useful Increment every Sprint

Those two words have specific meaning and it is important that they are recognized.  

I pulled these from Merriam-Webster's dictionary to satisfy my explanation.  You might prefer other definitions.

Committed is "having made a pledge or commitment to someone (such as a romantic partner) or something (such as a cause)"

Commitment is "an agreement or pledge to do something in the future"

Accountable is "subject to giving an account"

Account is "a statement explaining one's conduct"

The Developers pledge to do something in the Sprint that will result in an increment that satisfies the Sprint Goal.

The Scrum Team is subject to giving a statement explaining their conduct during the Sprint as it relates to creating an increment that satisfies the Spring Goal. 

So those statements are similar but convey completely different meanings. 

"Developers are the people in the Scrum Team that are committed to creating any aspect of a usable Increment each Sprint".

The Developers are accountable for the quality of the Increment as represented by the Definition of Done. Only they can do this because they are the ones creating it. They are doing the work.

"The entire Scrum Team is accountable for creating a valuable, useful Increment every Sprint"

The Product Owner, on the other hand, is accountable for maximizing the Increment's value. Hence the entire team is accountable for creating a valuable and useful Increment.

@ Michel D in addition to the previous responses, Developers turn sprint backlog items into usable product increments that  create value to all stakeholders. On the other hand, the Product Owner and Scrum Master  support Developers to turn Sprint backlog items into usable valuable product increments making the entire Scrum Team accountable for producing a usable valuable product increment aligned with the product vision, product goal and business objectives.