There is no connection to tharpanam on full moon day.
If a new month or eclipse occurs on a new moon day, tharpanam should be performed because it is done during those occurrences and not on full moon day.
Notes
Tharpanam should be done during a punya kalam based on the birth of a new month; if the new month begins in the morning one has to do tharpanam first and followed by thiruvaradhanam. If the new month begins after ijjya kalam, one has to complete ijjayaradhanam and proceed to do tharpanam.
As darsha shrarddham is done during the afternoon, our elders take bath in the afternoon to do thiruvaradhanam first followed by darsha shrarddham/ amavasai tharpanam.