When you say more so, it makes me think that it is still there to some extent when the car is warm.
I saw a post some time ago from Niki Gower of RTech who said there is an anti bleed back valve on the low pressure fuel line that can go weak allowing the fuel pressure to drop over time. So spluttering to start as the pressure builds up.
However, if you always have a bit of a problem, it probably cannot be that.
You will have APR software version 3.4. This is a generic map that takes account of the general hardware modifications for a stage 2+ car. A runner flap delete is not a standard 2+ modification so I am not sure the software can cope with this and so this is more likely to be your issue.
If you are within 30 days, ask for a refund and get flashed back to standard. You could then have a custom map that really will take account of the rfd.
If you don’t get a straight answer about this from your tuner, I would ask for advice from Awesome GTI as they are HQ for APR in the U.K. and in my experience are very helpful.
If Awesome confirms that the software cannot cope with the rfd but your tuner says it would have been fine, you have decent grounds for a refund.