If your kart is set up properly you will almost always be faster on newer tires. If you are faster on used tires that means the kart is over stuck and the set up is wrong. Now if you were using very very soft tires on a low horsepower class sure used might be better. But we don’t run those types of tires in the US and certainly not at club level.
If you’re new and still learning then used tires will be okay, you really have to be right on that razor’s edge to take advantage of new tires. If I were you I would record your set up right now on those used tires, seems like it works well for you. When you get new tires if you go slower, throw a softer axle in, shorter hubs, etc.
If you’re able to beat others at the track with those used tires, stick to it, save some money. But if you want to get the most out of the kart, tune it for the tires and you’ll be even faster.