Start sliding before the turnover, not after it. If your full-back is clearly joining the attack, the rest of the back line should already be adjusting their distances underneath the ball.
That does not mean you stand in the full-back position. It means the nearest centre-back becomes slightly more connected to that side, the other centre-back narrows with you, and the far full-back may also tuck in. You are protecting the spaces that would be attacked if possession is lost.
Once the ball turns over, your first job is to delay access to the most dangerous central or channel space while the full-back recovers. If you sprint all the way out to the touchline too early, you can open the middle.
Think of it as the whole line sliding together rather than you personally covering every metre the full-back has vacated.