Not correct. You are not supposed to become positive after vaccination. However, the claimed efficiency is around 92% so at least 8% of those vaccinated can still get the disease. In reality the actual efficiency is around 50% at best as shown by studies in Brazil. So around 25% to 50% of those vaccinated might still end up sick. Still, it is better than nothing as it reduces your risk by half or more.People can become covid positive even after both doses as there is no 100% efficacy. But AFAIK covid vaccines are developed in such way so that the vaccinated people who get infected they develop milder symptoms only and don't fall seriously ill hence preventing death.