What do you mean doubles? It's not rising geometrically, but arithmetically i.e. constant addition. (Actually it is geometric, with the "constant addition" dropping cycle on cycle, but the time constant of that drop might be longer than you care about, i.e. the L/R time constant of the transformer.)
C2 voltage is evidently quite low. Given how small L2 is, and the duty cycle, it will take some time to charge up. This is a CCM flyback.
Tim