Electrical – Transformer Isolation

The fluxes created by the primary and the secondary windings are not equal; your equotion \$\frac{V_1}{V_2}=\frac{N_1}{N_2}\$ is just an approximation.

If you connect a transformer to the mains, but not to the load, the current flowing through the primary winding will create some flux in the core. It's determined by mains voltage, frequency and primary winding inductance. If you connect a load to the transformer, the primary current will increase in a way to keep the core flux close to what it was without load.

An 'ideal' transformer has its primary inductance rising up to infinity, so the unloaded (magnetizing) primary current drops down to zero. But infinite inductance multiplied by infinitely small current results in some definite flux in the core.

I think your expectations are wrong. If the primary and secondary are isolated, you should expect to see some random voltage develop between them.

If the voltage between them were consistently 0 V, that would be a sign that they are electrically connected and that the isolation has failed.

As another answer points out, you may not want perfect isolation in order to protect the secondary from damage due to electrostatic discharge. But even so you might only constrain the floating voltage with back-to-back TVS diodes or a spark gap, which would still allow the voltage between the two sides to vary by 100's of V.

And many isolated systems won't have any such coupling at all. In fact if the isolation is for safety reasons they will likely have to pass a "hipot" test to show that 100's or 1000's of volts can be applied between the primary and secondary without appreciable current flowing.