No, this is not the case in ArM5. You find the rules you are looking for on ArM5 p.171ff.
Initiative is determined for hand-to-hand and ranged combat (p.171) as well as for spellcasting (p.174) or using an enchanted device (p.100), then each participant (individual or group) acts in decreasing order of initiative. Usually, but not always, spellcasting or device go later, because their initiative modifiers tend to be smaller.
Successful Fast Casting allows to break the Initiative order and react to a melee or ranged combat action just about to happen, preempting its completion by a spell.
But a magus with a high Quickness might sometimes be able to cast a normal formulaic or spontaneous spell before a soldier with low Quickness and a slow weapon can whack him. If the soldier goes first and hits, though, the unlucky magus cannot defend and may receive a grievous wound. Hence most magi will avoid such contests of speed with chopper-wielding brutes whenever they can.