For any coil, E = N*d(phi)/dt. Always.
If E is the applied voltage phi will be the flux produced.
If phi is the applied flux to the coil, E will be the emf produced.
Lets look at this step by step.
1. When there is no load on the secondary side (i.e. No load condition)
E is the emf applied to the primary coil, then the coil will produce phi flux in the core.
You can see that, if E is sinusoidal, phi will be cosinusoidal.
The coil will consume that much current as required to produce the phi flux.
since, phi = N*I / reluctance_of_core we can calculate what will be the current required to produce the flux phi.
This current is the magnetizing current.
But since there is cosinusoidal flux in the core, the same rule applies to the secondary coil and there will be Emf induced in the secondary coil given by
E2 = N2*d(phi)/dt.
2. When there is Load in Secondary.
When you connect load to the secondary, then there will be secondary current. The secondary current flowing in the secondary coil will produce flux phi2 which will be in opposition with the flux previously being produced by the primary coil (by virtue of the primary magnetizing current). So, in effect the net flux in the core will reduce to phi-phi2. But Since Emf E is still being applied to primary coil, it demands that the flux linkage of primary coil still be phi. So what happens is the current in primary coil increases so that it now produces the flux: phi + phi2 so that the net flux linkage of the coil (that is flux in the core) becomes: phi + phi2 - phi2 = phi again. The additional current required in primary coil to restore the flux will not be equal to the current in the secondary unless the no. of turns are same in both of the coil. Hence, the secondary current that flows when load is connected to the secondary coil will be reflected in the primary coil on top of the already present magnetizing current (not as a replacement for it).
I hope you can now see the inner workings and understand why the magnetizing current is always present. Too answer in short, the flux produced by the secondary and the flux produced by primary would exactly cancel each other but because there is additional magnetizing current in primary, there will still flux in the core (hence the electromagnetic coupling)
I hope that wasn't too messy. I wish I knew LaTex.