This could vary from person to person and from issue to issue. There are different reasons to inject filler around the eye such as under eye bags, under eye hollowness, upper eyelid hollowness, and upper eyelid laxity and droopyness. Filler needs to be injected in different ways to correct each of these issues. That is why there is no standard way to inject filler that is applicable for every issue.
Different people will react to filler differently. Some might swell a large amount, some might not swell at all. Some will not bruise at all, some might have significant bruising. Sometimes it is just luck, other times people might have a propensity to swell or bruise.
It also takes filler a few weeks to soften up and feel more natural. In thicker skin areas this is not a noticeable issue, but around the eye the filler might be palpable and sometimes noticeable for a few weeks.
Injections around the eyes should be taken as seriously as surgery at times. True, a majority of people will look great almost immediately and not have any problems, but a small number of people will have significant swelling and bruising. Make sure you are mentally prepared to maybe be one of those people before deciding to have injections around your eyes. Just because your friend came to me and looked amazing the next day doesn't mean that you are guaranteed to have the same result.