The children are believed to have had little or no contact with others outside their families and were shown jihadist videos by their parents, police said.
"The perpetrators allegedly committed SARA (an acronym for hate speech about race, religion or ethnicity) through Facebook and was then secured by Aceh police officers on Monday, May 14, at around 11:45 pm", Aceh Police spokesperson Misbahul Munauwar told Detik today.
The coordinated attacks in Surabaya with their mix of military-grade explosives, and women and children being used as cover for suicide bombings, suggest a rising level of tactical sophistication in Indonesia's terrorists.
Surabaya police spokesman Frans Barung Mangera said the militant died in a shootout in a Surabaya neighbourhood with counterterrorism police, who had tried to arrest him over possible involvement in the attacks that killed at least 13 people.
Daesh claimed responsibility for all the attacks in statements carried by its Amaq news agency.
According to police, the accused Oepriarto was friends with the other family who carried police headquarters bombing out Monday's and a third family who died after homemade bombs exploded in their apartment on Sunday night.
The flurry of bombings raised concerns that previously beaten-down militant networks in the world's most populous Muslim-majority nation have been reinvigorated by the return of some of the estimated 1,100 Indonesians who went to fight with the Islamic State group in Syria.
"For the kids, I think this is craziness", said Taufik Andrie, who runs an Indonesian institute that helps rehabilitate former militants ready to rejoin society.
Officials have identified Oepriarto as the head of Jemaah Ansharut Daulah (JAD), an Indonesian IS-inspired network. All six members of the family were killed.
The use of children in the attacks has been particularly horrifying to people.
Another family reportedly attacked a police station this morning, wounding 10 people including police officers. Its leaders were killed in police raids and hundreds of militants were arrested. Their mother Puji Kuswati attacked worshippers at another church with her daughters aged 9 and 12. Another bomb exploded on Sunday evening in Sidoarjo, East Java, which killed three suspected terrorists.
Tito said it was the first time that terrorists in Indonesia had taken along children in their suicide bombings.
At Surabaya Centre Pentecostal Church, Futrianto then drove his auto onto the church grounds and detonated explosives.