There are several factors that could be thought to affect the performance of a multi-winding transformer.
a) the handedness of each winding
b) the polarity of each winding with respect to the others
c) where each winding starts and finishes
In practice, the handedness of each winding, CW or CCW, cannot be specified, as there is no reference! If you hold the core this way up, any given coil may be CW. However if you hold the core the other way up, it would be CCW. Which is right? The magnetic circuit is a loop, it doesn't have a 'this way up' end!
If you take the first winding as the reference, and record whether the other windings use the same or opposite handedness, then there is no observed influence on the performance of the complete transformer (but see caveat below).
If we choose one coil as a reference, and then record whether each other coil is wound in the same of the opposite direction, then we have to define which polarity of the reference coil we are taking as reference. This needs one of its wires marking somehow, and a dot at the start is as good as any other. A dot at the start of each other winding completely defines their mutual polarity.
Starts and finishes
For some transformers, where inter-winding capacitance is important, it is necessary to know which end of a winding is nearest to another winding, or to the core. For the first winding to go on, we know the 'start' wire will have highest capacitance to the core, and the finish wire have highest capacitance to the next winding, or the interwinding screen.
We are talking about a transformer here. This is a structure that is very small compared to a wavelength of the signals passing through it, and that has a pair of multi-turn windings linked by a high permeability magnetic loop.
If we deconstruct the transformer to such an extent that it is a few turns of wire with a manifest helix structure with no loop of high permeability magnetic material, and drive it with a high frequency signal such that the windings work like antennae, then the full geometry of the windings will affect the performance slightly, including whether the windings are wound in the same or opposite direction.