Well if you called that function each frame, the camera's movement will increase by a certain number each frame, say this number is 1. So if the frame rate is 30 frames per second the camera will move 30 quants each second, if the frame rate is at 5 frames per second the camera will move at 5 quants each second, see the problem? The camera would be moving too slow at 5 quants per second. You want it to move at 30 quants per second no matter what. The solution is to multiply the variable by time_step as this would offset the value to make the camera move at 30 quants per second no matter what the frame rate, see the variable in the manual.

What you have effectively managed to achieve, I think, is by dividing the difference in the camera position by 10, making it move smoothly:

This camera code from the Kingdom Hearts tutorial is doing the same thing, if the frame rate is too low temp will be equal to 1 meaning that the camera will be set instantly to it's position, if the camera is running at a good speed temp will be around 0.5 (which is really what your /10 is doing)
Code:

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	temp = min(1,0.5 * time_step); //changing 0.5 will change how fast the camera moves, at 1 places us at target, this value is what allows the smooth movement
	camera.x += temp*(camera_move_to.x - camera.x);
	camera.y += temp*(camera_move_to.y - camera.y);
	camera.z += temp*(camera_move_to.z - camera.z);

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Code:

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/*FUNCTION handle_camera() {
	camera_pan -= mouse_force.x * 12 * time_step;
	camera_tilt += mouse_force.y * 8 * time_step;
	camera_tilt = clamp(camera_tilt,-30,10);

	camera.pan = camera_pan;
	temp = fcos(camera_tilt,-camera_distance);
	vec_set(camera_move_to.x,vector(my.x + fcos(camera.pan,temp),my.y + fsin(camera.pan,temp),my.z + 20 + fsin(camera_tilt,-camera_distance)));

	temp = min(1,0.5 * time_step); //changing 0.5 will change how fast the camera moves, at 1 places us at target, this value is what allows the smooth movement
	camera.x += temp*(camera_move_to.x - camera.x);
	camera.y += temp*(camera_move_to.y - camera.y);
	camera.z += temp*(camera_move_to.z - camera.z);

	vec_diff(temp.x,camera.x,my.x);
	vec_normalize(temp.x,16);
	vec_add(temp.x,camera.x);

	trace_mode = ignore_me + ignore_passable + ignore_models + ignore_sprites;
	IF (trace(my.x,temp.x) > 0) {
		vec_diff(temp.x,my.x,target.x);
		vec_normalize(temp.x,16);
		vec_set(camera.x,target.x);
		vec_add(camera.x,temp.x);
	}

	vec_diff(temp.x,my.x,camera.x);
	vec_to_angle(camera.pan,temp.x);
}*/

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