Does "attacks hatched at home by extremists "poisoning the minds" of killers on American soil" mean

It means attacks that come from inside the country that are inspired by foreign extremist ideology.

He is saying that the terrorism that the west is most at risk of is not from outside but from people inside the country who are influenced by extremist ideology.

His exact wording says that the foreign extremists are "hatching" (giving birth to) the attacks, by "poisoning the minds" of people (influencing them with their ideology) in the US to kill people.

So in his wording, the extremists are external, the killers are inside, and the external extremists create attacks in the US by convincing people inside the US to their ideology.

It's a bad, convoluted paraphrase of what Obama actually said.

This is what he actually said:

"And as groups like ISIL grew stronger amidst the chaos of war in Iraq and then Syria, and as the Internet erases the distance between countries, we see growing efforts by terrorists to poison the minds of people like the Boston Marathon bombers and the San Bernardino killers."