So you got a MAF from a VR6, it probably is operating properly, but not at the exact voltage the TDI ECU is expecting for a given airflow.
It might be something like the 2.0 MAF, but reporting lower voltages instead. See
http://www.geocities.com/tech4tdi/pages/maf2l.html
The weird thing is that if you're reading low, fueling should be cut back. But then you got a tune so who knows what the new maps look like but the tuner.