The way I understand it, the unit must finish its current skill cycle before it can perform a new action. The only exception is death. So, if it takes the unit two seconds to walk a step, he has to finish that two-second step before it can attack.
From my experience, is this:
it depends on what skill is currently on
stop/hold/produce skills = instant change
move skills = must be locked on grid. if between two spaces on grid move will continue till it reaches next square.
attack skills = when animation finishes+attack skill over, or instant change when target unit destroyed
morph/repair/build = end of each cycle (tick)
death = instant change overrides any skill