I suspect you just have to get used to the different sensations on the new bike, including is steering geometry, determining how much the wheel has to be turned for a given turn radius.
A different bike from what I'm used to always feels weird at first, particularly when steering. Heck, changing, say, the saddle height by more than an inch on the same bike can feel weird.
Steering is inherently counter-intuitive. After all, to turn right, you briefly steer left (whether consciously or not)!
These fat tires are inflated to low tire pressures, and have a high side wall height. Of course, that is going to affect handling. Anything that affects handling will give you a feeling, to which you react, to which the bike, in turn, reacts, amplifying the surprise.
Steering probably lags a bit on these fat tires compared to narrower ones due to the flexibility they introduce between the road and the rim. Say we are initiating a right turn. The front wheel briefly steers left, inducing a fall to the right which produces the necessary right tilt. At that moment, the steering is supposed to recover to begin turning right. If that recovery lags a little bit due to a squiggly, thick tire, that induced fall will continue a moment longer, leading to a sharper turn than anticipated.
If you feel you're going too sharp into a corner (say, right turn), you might subconsciously straighten the wheel slightly (effectively, making a slight left turn relative to the ongoing right turn). But that will induce a counter-steer that takes the bike tighter into the right turn, which then amplifies the original sensation.