Yes your observation of the process followed in Bangalore is correct. Moving on to answer your query, the earlier purchaser has assigned his rights to you through an Assignment Deed, where the flat he was intending to purchase will now be purchased by you after you pay the transfer fee to the builder, so basically you will be stepping into his shoes. All the rights vested in him as the purchaser stands transferred to you name through the assignment deed.
Now coming to your question, the seller would be the builder and you will be the purchaser, there would not be a consenting witness.
Next the subject of sale would the UDS along with duly constructed flat, shown in the schedule as "B" & "C" schedule properties.
By the assignment deed, both the UDS and Constructed flat stand assigned to you, therefore there is no need of a separate transfer deed in respect of the constructed flat.
This is accepted by the sub-registrar and he will not insist for the original purchaser to do anything before this sale is registered in your favour.