Transformer with opposite polarity in primary and secondary coil
There is no significance of the apparent winding direction of primary and secondary in a transformer, apart from the polarity. There is no additional performance difference. Consider that you can reverse the winding direction simply by calling 'the other end' of your winding 'the start'. Changing the name of something doesn't change the way it behaves.

When you're building something for which the polarity of the transfer between primary and secondary is important, within an oscillator, feedback system, or for a flyback, you control this by making sure you know which wires are 'starts' and 'finishes' of the coils.

Just a few people, who usually hang out on the tin foil hat and free energy forums as well, do pay attention to the 'helicity' of windings, and ascribe magical properties to this aspect of Tesla coils and wireless power transfer setups. You can safely ignore them.