base2 covered your question well. I'm just chiming in to relate my personal experience.
I have two road bikes, one is a touring bike with relaxed geometry and wider (35 mm) lower pressure (I run at 65-75ish PSI) tires. The other is a "racier" bike (not a crit bike, but more a stage race geometry - note that I put "race" and related terms in quotes because I don't race) with narrower higher pressure tires (23 or 25 mm run at 100ish PSI).
After riding the touring bike for a while, when I get on the "race" bike it feels twitchy and I have to be careful not to overcorrect, it is harder to ride no-handed, etc.
This could be what you're experiencing. It is a matter of getting used to the quicker response and adjusting your steering and balance inputs to take advantage of the greater precision offered by the racier bike.