Since there is no feline equivalent to the human A1c test, a fructosamine test instead will help positively identify whether or not your cat has hyperglycemia (high blood glucose numbers) or diabetes. In many cases, cats have elevated blood glucose levels due to vet stress or an infection or high carb food and suddenly, the owner discovers a couple of days or weeks later that their cat is no longer "diabetic" or might not have been diabetic in the first place.
The range for fructosamine does not correspond to the blood glucose range from a glucometer and there should be a conversion grid on the fructosamine test results which give a range (i.e. on some tests, 190-365 is considered "non-diabetic range"). In addition, the fructosamine is an average over 14 days. This long-term average helps rule out temporary or transient hyperglycemia vs. prolonged diabetic hyperglycemia.
In any event, the most important thing is getting the high numbers down first, including using insulin, if necessary (i.e. DKA). Home-testing will also let you know if you need to start/continue with insulin treatment after the preliminary diagnosis and a fructosamine test may not even be necessary.