We pushback and start engines at the same time. Once the pushback has finished, park brake on, the FO does the after start scan and then the After Start checklist is done.
After that flight control checks can be done at any point prior to or even at the hold (though usually done once on the taxiway unless LVPs are in force, and the viz is very poor, when we would do the control check at the hold). Once control checks have been done (and a few other things) the first part of the before take-off checklist can be completed so it makes sense to get the control checks out of the way early on.
A further question on this topic. Our company SOPs require us to wait 3 seconds between control movements, eg. ailerons left,
pause 3 seconds, ailerons right, pause 3 seconds, neutral.
This is also what is says in the manuals as a fault won't show up before that time. However, there seems to be some discrepancy on the rudders. Only the sidestick is mentioned in the manuals, not the rudder. Some people say it should still be a 3 second pause, some say not.
Anyone know the definitive answer? What does your company do?