the thing you are noticing is indeed the latency/serverupdate lag

if you target a mob while running to it and wait at least 0.5 / 1 second before actually pressing the cast button you will notice your alt(s) to cast immediatly.
this is also often the case when targeting the next mob in a multimob pull, the alts will usually tend to stand still for 0.5/1 second before casting on the new target

after some time you get used to it, when you know the mob you got targetted is gonna die in the next burst of spells, you can immediatly target the next mob.
by the time the last cast has finished and the mob falls over the server had enough time to transmit your new target to your alts.

nothing you can do about it....... its how the server works... same way how when pressing a casting spell you see it happen on your screen IMMediatly... but walking tends to somehow 'lag' .... spellcasting gets priority in server updates while movement and TargetsTarget update only after 0.5 seconds