Adding Cats back on truck...Need to change tune?

I bought my 02 sierra a few months ago. Since buying it I had the engine rebuilt to the same specs as before, however I have added catalytic converters back on the exhaust. When talking with former owner recently, he stated that the tune should be adjust because when he did the tune without converters, he "disabled that function" and that extra fuel would be dumped in a burn up the converters. Does this sound right? Is this something I could correct if I had a hand held tuner or laptop to tune with? It seems to run fine... This is a whole new concept for me and I don't understand the capability of tuners. If anyone has some guidance about what I should do, how to get started etc, I will gladly listen...Thanks!

List of engine mods etc.
243 heads milled .0030, flat top pistons 216-220 114 lobe center 560-560 lift cam K&N Intake 80mm throttle body greentop 42lb injectors headers, custom exhaust with high flow converters 4l65e transmission with corvette servo yank stock converter 4.10 rearend gears.

Scan the ltrims and afratio to determine that but I doubt it's gonna dump so much that the cats to bad.

Thanks for the input. I will have to find someone to check things out. I don't have a tuner and don't really understand what all I could do if I had one. They sound complicated.