Tennis, off-center hits?

Sounds like you just need to play/practice tennis more. Badminton has more wristy movements that may actually hurt your tennis game. Ball machine practice and hitting a wall might help. You could also benefit from warming up at the service line before you start hitting at the baseline. At the service line you are forced to hit the ball cleaner and with a little topspin, to keep the ball in the service box. That basically warms up your vision too, and you should see the ball better afterwards.