I noticed that in anime, almost every character make "jiii" sound when staring. Is this an anime only thing or do people actually make "jiii" sound in real life when staring? I understand that it is an onomatopoeia but I think that to use it in real life when staring is weird as you might not want someone to know that you are staring at them (since it is rude to stare at some one is it not?).
One common reason to say じーっ out loud while staring at someone/something is to intentionally signal what you are doing. Its implication depends on the context, but it's typically something like "I've been watching you", "Are you serious?" or "I'm interested in this". This is a bit childish act, but that is not to say adults never do this. Of course no one wants to say じーっ when they are seriously sneaking.
A childish or kawaii-type character in anime often say onomatopoeias out loud (e.g., saying わくわく when excited, or しくしく when sad). Such a character may also say じーっ innocently and unintentionally while staring at something. This is basically an anime-only phenomenon, but real people may occasionally speak like this, usually jokingly.