Raviji in his Srichakra navavarana pooja wrote about poojayami and tharpayami. He mentioned to do poojayami with left hand (offering flowers with left hand) and tharpayami with right hand (ie vishesha-argya tharpana with right hand).
But most of the people follow the other way. ie, flowers with right hand and tharpana with left hand. there is also another variation in this. Sri Sringeri mutt pathathi follows both flowers and tharpana from right hand simultaneously.
Today i spoke with one more senior upasaka, he told there are many traditions has same thoughts of Sri Raviji's pathathi. He says the Bhaskaraya Sampradhaya people who settled in maharashtra has the tradition of offering tharpana with right hand for the first tharpana made for srimatha three times before the start of navavarana pooja.
hope there are differences and similarities with this practice in various other sampradhaya. learned people here, please shower some light on this act.