if you're playing ziggs mid, you should absolutely be going for the kills, as you are the "apc" (ap carry). likewise with something like his ult, and his artillery burst dmg.. you shouldn't be holding back, and it's not up to you to do so if your teammate who believes "you shouldn't be going for the kill", it's on them.
if you're playing support bot lane however, alongside and adc - for one you'll eventually learn that in more serious matches people frown upon ziggs support.. i often play it myself, but only if im fooling around with friends in normals and never in ranked. and for two, when playing the support role seriously, if you CAN give up a kill, you should. but if its ever even remotely in question about whether the kill can be secured, you should absolutely take it to make sure they don't get away. even more so if you're playing something like a mage support/kill lane, as the kills benefit you about as much as the adc (tho i myself don't like this style of play)
you have to use your own judgement, you'll eventually learn what champs can escape or when they just used flash and have no means of getting away so you can just free give the kill to your adc and funnel gold to him like you should as a support.. or times where theres a chance they might flash/dash or get help, and you need to secure the kill as quickly as possible.
as i said though this is only for support, as when you're mid and you're ulting. you dont worry about a ks. now.. if you were to walk down to bot lane when bot has already pretty much assuredly gotten a kill, and just walked up and last hit auto'd an enemy that was clearly already dead, that's what "kill steal" really means, and you should pretty much never do that. especially given that toxic players will generally lose their shit over it and make your game hell a lot of the time.. best to just avoid it, but if your "ks" was justified (an ult from river to help) and they bitch about it, just take the kill and ignore them.