It depends on how sensitive they are to the allergen. Some reactions can happen instantly, some can take hours, some days, weeks or months. It really is hard to say. That is why allergies are so hard to diagnose sometimes.
Kona is allergic to a certain vaccination (Lepto.)nd she did not react to it until 5 hours after the second shot which she received 2 weeks after the first shot. If she ever gets it again it may kill her. Not worth the risk in my opinion.
Alot of times the initial exposure sets the body's sensitivity up and the next exposure could be deadly - as in bee stings.