Well you subtract a value each frame without using time_step at the end of this line:
camRollResult = camRollResult + (-dist.y * 1.5 * time_step) - camRollResult * 0.2;

If you smoothly want to adjust angles, use something as follows:

camera.tilt += ang(target_tilt - camera.tilt)*0.25*time_step; // the factor should be lower than 1
or if that is too fast use clamp:
camera.tilt += clamp(ang(target_tilt - camera.tilt)*0.25,-5,5)*time_step;

Now the adjustment will (possibly) start at maximal speed, so you would have to use a second variable/ a different approach, for example as follows (untested, maybe needs some bugfixing):

i = ang(target_tilt - camera.tilt)*0.25;
camera_tilt_speed = minv(camera_tilt_speed+0.25*time_step,minv(abs(i),5));
camera.tilt += clamp(i,-camera_tilt_speed,camera_tilt_speed)*time_step;