All Seeing Eye
Admiral
so that means...
peters wanting to help everybody makes it so he gets everybodys powers...
I think it goes deeper than that. As I said in another thread, I think some people get powers due to the way they think, such as Daphne with her leg problem gets the ability to run fast, Ando gets a 'sidekick' power because that's what he believes himself to be. However I also think in some cases the factor is Genetic, Parkman got the same power as his father, Meredith and her Brother inherited the same Fire ability which would also indicate genetics.
Peters ability to absorb peoples powers is very very similar to his Father Arthur Petrellis ability to take peoples powers, Peters ability is just a different mutated form of Arthurs ability which was likely passed down genetically so when Peter took the formula the genetic coding was still there within him and the formula just reactivated those genes.