All high spin rate projectiles, no matter if they are pellets or slugs, spiral when they leave the barrel. Usually the spirals will be very small so you will not notice them. If you have a perfect pellet/slug fired from a perfect barrel held by a perfect shooter, the spirals will be minute but anything less than perfect such as initial yaw rates, offset CGs or asymmetries on the surface, will increase the size of the spirals, but they will still be small close to the gun. What happens next will depend on the projectile design.
Considering pellets, pellets have a relatively low BC and poor dynamic stability. The poor BC means that as the pellet moves down range, the forward speed decreases at a much faster rate than the spin, giving a growing gyroscopic stability. The poor dynamic stability means the yaw the pellet started with will either stay much the same or increase. So with increasing gyroscopic stability, and growing maximum yaw angles you will start to get long yaw wave lengths and increasing yaw amplitudes which will give visible spirals. The range at which the spirals become visible will depend on several other factors such as muzzle velocity, twist rate and the design of the pellet.
Heavy pellets have characteristics which make them more prone to spirals. The centre of gravity tends to be further aft than on medium weight pellets, which reduces the aerodynamic moments due to the CG being much closer to the aerodynamic centre. This makes them more gyroscopically stable to start with, giving longer yaw wave lengths unless the barrel twist rate is lowered.
Cross winds can induce spiralling, particularly on heavy pellets, but you do
not need cross winds, they can do it themselves.
As to the original OP's problem, there are the usual methods for delaying the start of spiralling, such as reducing muzzle velocity, decreasing barrel twist rate. The Air Arms barrels and the Daystate barrels have relatively high twist rate barrels, so may be prone to the problem. I understand however that changing barrels may not be practical for the original poster. Trying to minimize launch errors, may help extend the range before spirals become a problem by reducing the muzzle blast or any of the other ways of getting a clean launch of the pellet.
I looked at pellet spiralling in this thread,
https://www.airgunnation.com/threads/pellet-spirals.1297114/, but it concentrated on .22 calibre. The information in the first half may be of use to you.
