Not quite. Each of us basically has our own “block chain” in RaiBlocks. I use quotes because it doesn’t meet the Bitcoin definition of a block chain, but it still is a linked chain of data blocks. The normal sequence is that user A records a “send” record and then user B records a matching “receive” record on their individual block chains to record the transfer of XRBs.
Normally, a RaiBlocks block chain should only have a simple, straight chain of records. The only time voting happens is when there is a conflict/fork in a block chain. If you watch that animation carefully (it is too fast), you’ll note the small moving blocks indicating what people believe is the proper transaction at different phases. Some believe the yellow transaction and some believe the green transaction. As voting happens, eventually they all settle on a single result. The losing transaction is simply ignored.
The representative accounts that we have in our wallets are for this voting. Each voter is weighted by the number of RaiBlocks they represent. The default reps available are supposed to be online 100% of the time to participate in voting. You can actually set your own account as your representative for voting. Note the using a representative doesn’t affect your RaiBlocks balance at all.
You already mentioned that the white paper is not clear on this, but for anyone that wants to read it directly, it is in section IV.G.