Yeah
Every car is different in the end
Fuel pressure regulator would make it run badly all the time he wouldn't be beating any skylines if it had low fuel pressure.

How'd the new filter go? Help at all or not?
At the end it dosnt hurt to change stuff like that just so you know everything is knew and doing its job.
Didn't break anything? :p

Ignition could be retarded is it really slow down low then kind of takes off once it hits 3-4000 rpm and not the boost side of things,
If your car has a dizzy you can adjust the ignition timing by turning the dizzy
I'm sure there's a thread on here you will need a timing light I would recommend leaving it for the tuner to play with as he will know what he's doing hopefully but my ignition timing is set at 15 degrees

So fuel filter didnt help at all? At least it's knew and clean, you may also have a blocked cat if your running one or are you running a dump pipe? Depending how old the cat is,

But if its just like an msd or something it's just a booster really,
Aslong as it still retains the distributor and leads its nothing really different
15 degrees is advanced i didn't do it tho previous owner did.
Stock on mine was 10 I believe

Also you wouldn't need a tacho to tell 45kms in second is about 3000
You would notice it e heaps sluggish down low then really pick up
My previous car had retarded if ignition timing was really crappy down low but it went for it at 3250 Ish
Timing belt was a tooth off and was running at 7 degrees
Fixed it to stock 10 then advanced jr to 14
And you could really tell it picked up quite a lot down low.
You would put your foot down from rolling off the line and it would big down jerk not really go anywhere then once it hit 3400 it would just throw you back hard and go.

So maybe your ignition timing is off or your belts a few teeth off?
Blocked cat if you have one?
I don't have any experience with a turbo so I'm I'm only throwing things I know from my car.

But check your timing. That's easy to do.

Exactly,
Check you timing might be too far advanced and it's leaning out, not sure what you want it at in a turbo in the performance manual by terry heick just leave it alone he says in turbos

Also your cat may have died on you if it's the original one it can happen the cores just heat up and break down and being a ceramic core it could be possible
Get that check
We had a yaris come in the other day at toyota whose cat had died and caused the car to run just like yours. Blocked the exhaust.

If its none of those could be the tune
Or an O2 sensor that's why you should get the codes pulled if it has any that will tell you if it's anything to do with what the ecu controls :)

So car has been tuned for a week now, but I still have the idle problem whilst cold, and when I drive it cold and accelerate it will just stutter and not really go anywhere. Anyone have any ideas?

was the car tuned for a cold start at all??? this is usally done on a cold engine obviously and preferably at the same temp. as the early morning or a similar scenario. to get it right. or the tuner will put in values thats have been used before as a guess