At first it seems odd that Gensei could upload a virus onto the Misaka Network through Misaka 10032, since only Last Order is supposed to have upload rights — in fact, the whole point of Last Order's existence is to prevent exactly this kind of thing. However, the clue lies in Shokuhou's earlier mention of using Misaka 10032 to place mental safeguards around all the Sisters. It seems the Misaka Network linkages between them gives Mental Out access to the minds of all the Sisters, even if doesn't grant access to the network itself note (like tunnelling traffic through a computer network. So what Gensei presumably did, once Exterior gave him the Mental Out power, was use Misaka 10032's connection to take mental control of Last Order, and transmit the virus through her.
