Electronic – Crosstalk between secondary transformer windings

The Farnell page has a little better description of the wiring needed:

Primary Pin Connections        |    Secondary Pin Connections           
Style   0V  115V    0V   115V  |    0V  Vsec    0V  Vsec
UI39    1   4       9    6     |    17  19      14  12

It looks like connecting per this table parallels the primary winding to set the turns ratio for 115V input.

Based on that idea, it looks to me like pins 1 and 6 should see the AC and pins 4 and 9 should be connected together, to maintain the correct phasing of the primary.

What you may be getting confused about is the "ideal transformer" in the equivalent circuit. You should not regard it as having any magnetic qualities at all. Try and see it like this: -

Whatever voltage you have on the input to the ideal transformer, \$V_P\$ is converted to \$V_S\$ on the output of this "theoretical" and perfect device. It converts power in to power out without loss or degradation such that: -

\$V_P\cdot I_P = V_S\cdot I_S\$

The ratio of \$V_P\$ to \$V_S\$ happens to be also called the turns ratio and almost quite literally it is on an unloaded transformer because there will be no volt-drop across R3 and L3 and only the tiniest of volt-drops on R1 and L1.

This means you now have a relatively easy way of constructing scenarios of load effects and recognizing the volt drops across the leakage components that are present.

The equivalent circuit of the transformer is really quite good once you accept that the ideal power converter is "untouchable" and should just be regarded as a black box. For instance you can measure both R1 and R3 and, by shorting the secondary you can get a pretty good idea what L3 and L1 are. With open circuit secondary you can measure the current into the primary and get a pretty good idea what \$L_M\$ is too.