Correct, if the vote is positive (50% quorum from the network) means the transaction is valid and accepted.

The representatives kick in when there is no quorum from the network, they vote in case of disputes on transactions, which according to the Nano team is about 1% of the time.

Each round of voting takes approximately 15 seconds, and the maximum rounds of voting is set to 4 (1 minute) at which time the chain takes on transaction and accepts it as true while rejecting the other (only in case of disputes).