Turn the gun on, turn the eyes off, air it up.
Hold the trigger down. Does the back block stay back?
If so, it is in CLASSIC mode, not regular semi.
Regardless, check the mode by entering the setup menu and ideally, set it to FACTORY FAST. This may cure it.
Does sound like its in classic though.
Also...what do you mean it starts in training mode, then starts firing normally? Is this aired up? If its in training mode, then it will stay in it...if you mean that the back block moves but you don't get a bang, then when you fire faster, its starts to bang, then see the above and defo set to Factory fast.
The other thing it could be, having thought about it for more than 5 seconds, is that your SON time is too low. This means that it may take more than one pull of the trigger to release the hammer.
So you may need to increase it (people lower it to try and speed the gun up). Factory setting for it is 4ms. You may also have your Lug wound in too far.