The centre had not set when it came out
CommonA baked cheesecake is a custard, and its centre is the last part to reach setting temperature. It should leave the oven with a small area at the middle that still wobbles as a single mass, because residual heat carries that region through setting as it cools. Taken out while the centre is still fluid rather than wobbling, there is not enough stored heat to finish the job, and chilling only makes the fat firm — which feels like setting until it is cut and the middle runs.
What to change
Take the custard out while the centre still wobbles
Look for the edges set and a circle at the centre — roughly the size of a coin for a quiche, a little larger for a cheesecake — that still moves as one mass when the dish is nudged. It should wobble like set jelly, not ripple like liquid. Take it out at that point and let it finish on the bench.
Quiche, baked cheesecake, custard tart, bread pudding — any baked egg custard.
Trade-off: It requires judging a moving surface rather than following a time, and an oven that runs hot will reach it sooner than any recipe says.