Most issues won't pop up overnight, though they could in theory. Most of the time it would take days (or sometimes even weeks) for symptoms to appear. Watch for lethargic fish, loss of appetite, cloudy eyes, dashing/scratching/flashing, shedding slime coat, etc. It could bring in any number of things with a range of symptoms.
I quarantine all new fish, regardless of where they came from. If they're wilds, I tend to treat them for roundworms, flatworms, and intestinal flagellates before introducing them to my existing stock. Once you've had a new fish wipe out your entire stock, you'll make it a priority. It's not if, it's when. Buy fish long enough and one will eventually bring home something (ich, parasites, columnaris, etc.).