Add the ginger, oil, tamarind paste and water to a blender. Puree. You may have to fight it a bit depending on your blender. Scrape it down the sides if needed. You will get there.
Toss in the tandoori masala and pulse to combine. Scrape it out into a bowl. Stir in the citric acid. This gives the tandoori paste tang.
Taste just the smallest amount. It's pretty strongly flavoured. Decide if your tandoori paste needs salt. Some masalas are saltier than others so you have to figure this one out on your own. Choose wisely. Some are way too salty.
The ginger taste is pretty forward the day you make it. If you can, store it in the fridge for a day before using. This isn't critical though so don't worry too much about it.
Notes
This will keep a few weeks or more in the refrigerator.