There are 4 pins for the secondaries, 2 for each one and they are not internally connected.

Heres the datasheet if that helps. The part number is VTX-121-4810-212.

I read somewhere on the internet that the amps given are for both secondaries total. Im just doing the maths though and 10VA / 12V = 0.833A. The value given for that coil is 416mA which is half 0.833A. I think this means that each secondary is capable of 416mA and using both together will give 833mA.