Vrish Sumbh Nishumbh killed by Jagatdhatri..u can see the murti..they have 2 asurs...n in begal Mahalaya k din tv n redio pe Mahalaya k programe dikhaye jate hai jis main Raktbeej,Sumbh Nishumbh n Mahishasur ki story dikhayi jati hai..woha pe bhi dekhate hai that S & N killed by Parvati's Jagatdhatri roop...n then comes Mahishasur...Durga Puja ka asli time hai March jise Basanti Puja k name se jana jata hai..October main jo hota hai use Akal Bodhon bolte hai..Shri Ram ne Ravan se jitne k liye samay se pehle Shakti ki puja ki thi...n uske bad se Durga Puja usi time pe hota hai...
You seem to have the sequence scrambled. Jagadhatri puja comes weeks after Kali Puja.At any rate, Shumbha, Nishumbha, et al are not what's celebrated in Durga Puja. It's Mahishashur. I think Kali Puja coincides when Shumbh & Nishumbh were killed, unless it marks Bhadrakali slaying Darukasura rather than Mahakali slaying Raktabheej.