Not really true from what I have seen, the smaller turbo will flow some exhaust gas which will then go onto the bigger turbo, but typically the smaller turbo will also have a wastegate (either internal or external) to allow much of the exhaust gas to bypass it completely to prevent over spooling it, and both the gas that has gone through the turbo and the gas that has gone down the wastegate is then directed back into the exhaust inlet of the bigger turbo.