Have you received and email saying you have payed from the DVLA - normally send you a receipt asap.
Also download the app called MyGarage or something - it shows all details of the vehicle including if it is taxed - to double check everywhere and to make sure.
But definitely look for a receipt from the DVLA... they normally send it out asap and call them if you wanna make sure.
just yesterday I had bought a new car. I've done the tax the same night online but it still showing as its still sorn the next. I dont wanna get clamped so would I be alright as long as I've paid. how long does it take to become updated.