Edit: Beaten to it
.
Right, As standard the starlets air intake system and exhaust are very restrictive. When you remove the cat and fit a decat some restriction is removed and even more of the restriction is removed when you fit a better flowing exhaust as you have.
When you remove the standard air box and fit an open filter again more restriction is removed.
All of this restriction being lost will leave the engine take in air easier and throw it out of the cylinders through the exhaust easier. This also means that it will cause your turbo to produce more boost than standard due to the less restrictive setup. This extra boost is now triggering a pre-set safe limit which, is programmed into the ECU and is called fuel cut or boost cut. When you create more than roughly 0.85bar the ecu will cut the fuel going to the engine and cause your spluttering.
The remedy is to fit a FCD which wires into the ECU and fools the ECU into thinking it is getting less boost than it realy is and thus eliminated the boost cut. There is still a problem though because if you simply fit a FCD the extra boost you are running over fuel cut say 1 bar will not be fueled for by the ECU and you could end up running lean and get fried pistons. This is why you need a RRFPR (rising rate fuel pressure regulator) preferably a full Sard kit which costs roughly £135. The RRFPR is adjustable so you can set the base fuel pressure higher than the standard 2.3 bar of pressure. Not only do you get an increased base pressure but the regulator is connected to the inlet manifold with some vacuum piping and when your car creates boost some boost pressure travels down the pipe and increases the fuel pressure further as the boost increases and provides the extra now needed fuel.
To sum up;
If it is fuel cut you are experiencing (more information needed on exactly what happens when the light comes on and it splutters) you need to buy a FCD and a RRFPR and then run 1 bar of boost, or adjust the actuator down and hope that it cures your problem but this may not stop the fuel cut because you may be experiencing boost creep which is common after fitting a free flowing exhaust and decat.
Hope this helps
Dave