You slide a probe into the roast and it reads 60 °C. Perfect: that is the pink you wanted. You lift it out, set it on the board, and check again five minutes later. It now says 66 °C. Nothing is heating it. So where did the extra six degrees come from?
An oven does not heat a roast evenly. It heats the surface, and the surface hands heat inward by conduction, one thin layer at a time. Meat is mostly water and conducts heat slowly, so the inside lags far behind. While the roast is cooking, the temperature runs from hot at the skin to cool at the core.
The moment you take it out, that slope is still there. The outer layers are far hotter than the centre, and they now have two places to send their heat: out into the cool kitchen air, and inward toward the core. The outside loses heat to the air through a thin surface layer, but the heat headed inward has a cold centre to warm. For a while the inward flow wins, so the centre keeps climbing even though the oven is gone. That is carryover cooking.
This is a model of a roast cut in half, from the surface on the left to the centre on the right. The top graph shows the temperature at every depth. The bottom graph tracks the centre over time. The dashed line is a 60 °C target. Press Take it out at the moment you think the centre will end up at 60 °C, not the moment it reaches it.
Run it a few times. Pull a thin roast late and it overshoots by only a little. Pull a thick roast at the same centre temperature and it keeps rising for much longer. Then lower the oven and try again.
Two things set how much carryover you get. The first is the steepness of the slope when you pull. A 240 °C oven drives the surface far above the core, so there is a big store of heat waiting in the outer layers. A 100 °C oven keeps the whole roast closer to one temperature, so there is almost nothing left to flow inward.
The second is thickness, and here the rule is harsher than you might expect. Heat spreads by diffusion, and the time it takes to cross a distance grows with the square of that distance. Meat is mostly water, so its thermal diffusivity is close to water's, around 10⁻⁷ square metres per second. Plug that in and heat needs on the order of ten minutes to travel one centimetre. Double the thickness and the trip takes about four times as long. That is why a thin steak settles within a couple of minutes while a big roast keeps climbing, and then stays warm, for a long time.
Pull the meat before it reaches your target, and let it rest while the heat evens out. For a steak the gap is small. For a large roast from a hot oven it is bigger, and the best answer is to watch the centre temperature with a probe, not the clock. The USDA's safe minimum for whole cuts of beef, pork, lamb and veal is 145 °F (63 °C) followed by a three-minute rest, and for poultry it is 165 °F (74 °C); the rest is part of that recommendation, since the meat keeps heating while it sits.
One caution about the model above: it treats the roast as a flat slab with fixed properties. A real roast has a shape, bones, fat, moisture evaporating from the surface, and an oven that behaves differently from air at a fixed temperature. The shape of the story is right, but the exact degrees are not. Your probe, and a little practice with your own oven, will beat any simulation.