Mr. Adesina stated this Monday morning on Channels Television during its Sunrise Daily programme.
At least six persons were killed in Goska village, Jema’a local Government Area in the early hours of Christmas.
The victims included a teenage secondary school student, Gimbia Morik, daughter of a former council chairman in Jema’a.
The killings, by suspected herdsmen, occurred despite Jema’a and two other local governments – Kaura and Zango Kataf – being under a 24-hour curfew.
The state government after a meeting of heads of various security agencies in the state, had on December 21 imposed the 24-hour curfew to prevent violence during the festive season.
Scores of people have been killed in ethno-religious violence in Southern Kaduna in 2016.
As the killings continue, Mr. Buhari had come under criticism from Nigerians for his silence.
Citing Nigeria’s federal structure, Mr. Adesina said there was no need for Mr. Buhari to speak since Mr. El-Rufai is “on top of the matter.”
The presidential aide said as the chief security officer of his state, it rests on Mr. El-Rufai, who has pledged to bring perpetrators to book, to deal with the matter.
“You don’t have to hear from the president on that matter. When it pays us, we talk about federalism and true federalism; yet you want the president and presidency to talk about everything,” Mr. Adesina said.
He also said “when a thing like this happens in a state, there is a chief security officer and he is supposed to be on top of the matter.
“Governor El-Rufai Rufai was at the villa on Thursday to brief the president, so why should the president then be talking about it?
“True federalism is the governor should be in charge and he is in charge of it,” he said.
The killings in Southern Kaduna are suspected to be due to violence between the locals and migrating Fulani herdsmen.
Apart from Kaduna, similar violence between locals, mainly farmers, and migrating herdsmen has caused the death of hundreds of people in several other states including Benue and Taraba.
Mr. Adesina on Monday said local authorities must play a crucial role in stopping the violence.
He said state and local governments have a major role to play in dealing with herdsmen crisis.
He said Mr. Buhari is always in constant touch with governors whenever an attack occurs to get timely updates.
The spokesperson said Mr. Buhari has consistently maintained that the best way to stop the killings is through collaboration between the states and the grassroots leaders in local governments.
“The federal government has roles to play but not as much as the state and local governments,” he said.