Keeping in mind that I only opened the mission in fred and have not played through it in years.
It looks like you have to destroy the SC Jazirian, SC Ahriman, Rama, Arjuna, Krishna, Vishnu, and Indra before the Kintyre will arrive. They all have to die for the shivans to commit a corvette.
Just played it, and it looks like the default layout of loki + subach + Prometheus R + Hornet, is just insufficient to kill all the ships. I would suggest picking the herc with Prom Regular + Subach + Hornet + Tempest. Use the tempests on the cruisers and the hornets on the fighters. There's just no time to take everything down with primaries.