When/where to open and close a transformers output
The arguments against zero crossing switching transformers applies to primary of secondary.  The claim (largely borne out in practice) is that the core saturates when subject to the rising voltage while unmagnetised. This is generally not an intuitive outcome. It makes sense when you consider that in an inductor under steady state conditions voltage and current are 90 degrees out of phase. By switching the voltage on at the peak of the voltage waveform you have maximum voltage and zero current so the 90 degree relationship is automatically established as the initial condition. You still need to build the "magnetising current field" but you are at the best starting point.  

Nicely summed up in the final reference below:


  Instead, it would be better to close the switch at the peak of the
  input AC line voltage. Since the inductor's current is initially zero
  as before, switching this way puts the applied voltage and the
  inductor's current immediately in quadrature with each other (or
  really close to it) and there is no transient event or current
  settling phenomenon.


The current starts out already settled.

At a minimum what happens is that the current waveform is offset relative to zero so that a current sinusoid DC offset by Ipeak/2 initially occurs. This leads to about double expected peak currents if the core does not saturate - and some sources suggest even higher initial surges, due to saturation effects. 

The subject is covered reasonably well in Rod Elliot's inrush current -
and especially section 4. "Inductive &amp; Transformer Inrush". 

Useful paper here - less severe claims
Effect of Switching angle on Magnetizing flux and Inrush current of a Transformer
(ie saturation effects not dealt with) 

Open electrical wiki - transformer inrush

Some practical experiences reported here To Zero Cross or Not To Zero Cross.   

He comments:


  Some years back, I was the project engineer on a large component
  burn-in system. The system was supplied off of a 3-phase power
  transformer so that the loads could be as balanced as possible. I had
  designed TRIAC controllers to ramp up the line voltage to minimize the
  line surge with +90 degree phase shifting. Each power supply was a
  very large, 50lb, power transformer with multiple secondaries. To tell
  a long story in short, the 'chief' engineer insisted on replacing the
  three small power transformers I had specified with the one big
  monster and he also insisted on using zero cross over phase control to
  minimize the current surges despite my arguing for the other method.
  To him, zero voltage across the primary meant zero current....
  
  The PC boards were finished per the Chief's changes and a few power
  supplies were built. When they were switched on, there was a snap and
  flash of light in each one of them, a PCB trace was vaporized due to
  the huge magnetizing current resulting from the zero cross over phase
  control. Since the boards had already been built, modifying them was
  out of the question, the only thing I could do was to place a large
  ballast resistor in the primary to limit the current surge. The Chief
  refused to accept the premise that it was his zero cross over and
  monster power transformer causing the problem.