Warm the milk to blood temperature and no further. Milk hot enough to feel warm on your wrist will kill the yeast, and a dough that never rises is the commonest way this bake goes wrong.
Enriched dough proves more slowly than plain bread dough. Judge both proves by size rather than by the clock.
For the overnight prove, 8 to 12 hours in the fridge is the working window, and the buns need 1 to 2 hours at room temperature the next morning before they go in. Baking them cold is what leaves you with a dense middle.
To make them the same day instead, skip the fridge and prove the shaped buns in the tin for 45 to 60 minutes, until puffy and touching.
Do not keep the baked buns in the fridge. Cold air stales them faster than anything else will. Airtight at room temperature, or freeze them.