I am not a roadway expert (I think that robby has more expertise with this), but I have been designing and specifying paved surfaces for over twenty years, and have been on more paving inspections than I can remember. A roadway paving expert may not be able to answer your question; it may be more geared toward a racing expert.
In the Northeast, paving is traditionally done with bituminous concrete pavement, now renamed “hot mix asphalt” or HMA (presumably renamed so that all the manuals can all be reprinted at taxpayer expense to reimburse some pol’s nephew). The mix is a specific gradation of aggregate (gravel or crushed stone) with a percentage of bitumen (typically 4-8%, depending on the particular application). Stone size is larger and bitumen percentage is less where more bearing strength is required. This is called the binder or base course, placed on a compacted gravel course. As you might expect, this will leave a coarse looking surface that is also hell on tires. So this structural layer is then topped with a mix that has smaller stones and more bitumen (the top or wearing course). While this does certainly have some bearing strength, it is primarily to provide an acceptable driving surface.
As stated above, the mixes come heated from the batch plants, and are placed while still extremely hot. The bitumen coats the aggregate and causes it to adhere to itself and damn near everything else within 20 feet of the paving job. After placement, the pavement is rolled for as long as is practical, usually an hour or two. This is to make sure that the aggregate is compacted as much as possible, and to fill as many voids as possible. After rolling, cars can drive on the pavement. I’ve seen cars allowed on pavement in less than an hour when necessary, but most good pavers prefer to leave this for a longer time, if allowed.
The above was for a new paving project, but it isn’t all that different for an “overlay” job. Sometimes a new top course is placed directly over the old top course if there is no concern as to the raised height of the roadway. Otherwise, the existing surface is cold-planed or milled down a certain amount (as danceswithcats referenced), and then repaved with new top course.
Over time, bitumen in pavement will slowly “dry out”, losing some volatiles. Therefore, standard practice for overlays is to have a truck spray asphalt emulsion over the old surface to provide a “tack coat” prior to placing the overlay. The thought is that the old bituminous pavement will absorb some of the bitumen from the new pavement, thereby robbing it of some of its use in the new pavement. The jury may be out on this practice: I have heard experts argue that it is pointless and a waste of money. However, most engineers feel that it is better to be safe, especially if the existing pavement has some age to it.
It would be interesting to know if the pavement was completely removed and replaced, or whether it was an overlay. If completely replaced, the waiting period might be to discover if inadequate compaction left loose areas that would cause the pavement to deform or sag.
If an overlay, then I am stumped. In normal roadway or highway paving, no “curing” is required. However, it is unusual for them to see the intensity that racing courses see; hence my original reference to asking a racing expert. If this is standard practice in the race industry, I can only surmise that it is to let the bitumen dry out a bit to ensure that the pavement will not deform under intense racing.