If the trigger is a double phase trigger that will fire the gun when the rear trigger is not "set", the trigger assembly is installed too deeply into the stock.
To determine if the triggers are double phase without removing them from the stock, remove the lock from its mortise.
Then, look thru the hole in the stock that the sear arm sticks into when the lock is in place.
If pulling the front trigger raises the blade on top of the trigger up so it can easily be seen, the triggers are double phase.
By lowering the trigger assembly in the stock by using shims or similar items, the rear triggers blade will be lower so it no longer is pressing on the sear arm when it is in the unset condition.
Some double set, double phase triggers have an adjustment screw for the rear trigger spring.
It allows reducing the spring pressure which can help to prevent the problem your having.
IMO, if the trigger assembly is a double set, double phase trigger a more professional fix for the problem is to grind off some of the top of the front trigger's blade.
The way factory set triggers are designed, they usually have extra material on top of the trigger blades so filing them to fit the gun being built is usually required.
If the trigger group is a Single phase, it is designed to only fire the gun if the rear trigger is first set.
Single phase triggers cannot fire the gun unless the rear trigger is first set because the front trigger does not have a blade on the top.
These single phase triggers are purposely made to always be pushing up on the sear arm UNLESS the rear trigger is set.
Setting the rear trigger lowers the blade down so it is temporarily no longer pressing on the sear.
The idea of a single phase trigger always pushing on the sear arm when it is unset is because with this trigger design the lock does not have to have a fly in it to work with the set trigger.
By pushing on the sear when the rear trigger is released, it keeps the nose of the sear well away from the half cock notch. Of course, this makes the half cock notch rather useless but at least the lock will work with a set trigger.
If the trigger assembly is a double set, single phase trigger, it is working like it is designed to work so there is no easy way of fixing the problem except to learn to live with it or replace the trigger assembly with a double set, double phase trigger.