I think what we can say for certain is that some feel you would know, and others feel you would not know. Which way you land on that might inform how you ultimately rule it in your game and what situational problems you might have to subsequently deal with.No, you do not know instantly. It's when you sit up and your head hurts that you realise you have flu. It's when you are doing your last rep when you feel your muscles ache. It's when you try to do something that you notice a problem.
Chances are, an intelligent person will notice something is up within a few minutes, but a few minutes is usually plenty of time for the party to do what they wanted. And an unintelligent target - e.g. a guard dog - is never going to wonder why they don't feel 100%.
Beyond the question of how one pictures hex, a DM might want to consider what problems arise from ruling one way or another, and whether the spell in question should be played under the stronger or weaker interpretation? For example, I saw hex in play across many game sessions and in the early and mid-tiers it seemed really solid. My players used it constantly and seemed satisfied with the impact. So for me, I wouldn't be looking for a stronger interpretation. Additionally, I would question why I'd want the problems an invisible cast seems to lead to? But if I felt hex was too weak, and if I either didn't mind those problems or saw other problems - or indeed, opportunities - I might go for the other interpretation.