Proper connection of choke coil in ethernet magnetics
My understanding of the common mode choke is that it works to prevent RF noise from entering from outside, as some Ethernet runs might be a hundred meters-by noisy power wires, and stops harmonics from the PHY drivers from getting outside and possibly violating FCC rules regarding EMI emissions.

The common mode chokes would serve no purpose on the PHY side, and I have seen no schematics with them on the PHY side. The PHY side actually must be as a clean as possible with just bias resistors at most. The PHY side drivers expect a very short connection directly to the magnetics. Designs vary so not all center taps are used.

Also I cannot say that nobody ever has or ever will use common mode chokes on the PHY side, with many designs being proprietary with no public release of certain details. As long as the PHY drivers can behave as they should I see no problem with that topology.

On the outside the center taps allow for PoE to be used without corrupting high speed data on the twisted pairs, as the supply current is common to both wires and at the magnetics it cancels out so no DC offset current is passed to the magnetics.

Usually twisted pair 'A' carries one side of the DC power and pair 'D' carries the other side. The 2 middle pairs are grounded unless the ports are rated for 1GB Ethernet.