The stock tires wont make noise on most surfaces and wont leave marks so you probably are spinning. If your traction control is disabled but advancetrac is still on then it may be applying the rear brakes as well when you start getting a bit sideways. Like above poster said you can come to a complete stop, hold brake and hold the traction control button for 5-7 seconds and it will turn advancetrac compltely off.

Get better tires for one. Aftermarket tunes make the throttle tip-in more aggressive to get rid of the lazy feel of the tranny. This means that the throttle and tranny pressure rise much faster as you push the throttle down, much faster than when compared to stock. This means that you need to retrain your foot/brain to go easier into the throttle than before. Stock tires are not really well designed to handle it.

I would not recommend turning off the traction control until you can get the car to not flip out on you when you step on it. Otherwise your next thread might be about how you fish tailed it coming out of a turn after you planted your foot in it. Not wishing that on you, just saying that could be the outcome.

I had the exact same issue when I tuned my auto car several years ago with Stock tires. The rear would get squirrely on me if I was slow rolling and stepped on it. Upgraded the tires to summer tires and retrained my foot/brain, no more issues for me unless I want it to happen.

^^This, and if it's wheel hopping, you need UPR Products control arms.

You can definitely be spinning the tires and not know it, I had an 13 AT and it did that a lot when I got on it with the stock pirellis.
Also from what I remember from reading the manual, the TC/advancetrac has 4 settings: On, TC off, Sport mode, and everything off. Sport mode has TC and stability on, just less sensitive so it lets you do more before it kicks in, but it will still kick in and stop you from completely losing control.