Rebloom in daylilies does not happen from the same growing point that produced the fan of leaves with its scape. A daylily growing point produces a fan of leaves and one scape but cannot produce any more leaves or scapes because it is completely used up in producing its scape. The leaves that are produced after the growing point develops into the scape are formed by a new growing point that develops. Usually the new growing point is right next to the scape. That growing point produces new leaves that look exactly like the leaves produced by the previous fan when the daylily is growing continuously but when the daylily is growing discontinuously the leaves that are produced by the new growing point are much smaller to begin with than the oldest leaves that were produced by the previous growing point.
Rebloom in daylilies happens from new growing points which produce their own sets of new leaves and a scape. Those new leaves are not distinguishable from the previous fan of leaves when the daylily is growing continuously but are distinguishable when the daylily is growing discontinuously. Rebloom is never from the same "fan" although in continuously growing daylilies the different fan lineages are usually impossible to tell apart.
On the diagram above leaves labelled 1a to 11a and the scape labelled A belong together as fan A. The growing point of fan A produced all 11 leaves and the scape but when it produces the scape it becomes smaller and smaller until it finally is completely all used up. The last little bits of the growing point are near the top of the scape. The crown must then develop at least one new bud or growing point so that it can continue growing. In the diagram the new growing point is labelled B and the leaves 1b to 11b are produced by growing point B. If growing point B starts growing immediately when the previous growing point A started to form into a scape then that is continuous growth and the B leaves will be the same size as the largest A leaf and they will all look like one fan of leaves. If growing point B becomes a scape and flowers in the same growing season that the A scape flowered then that is rebloom. If it only produces some of its leaves in the same year that the A scape flowered and some of its leaves in the next growing season, along with its scape in that next growing season then that is normal bloom. If growing point B does not start to grow then it forms a bud and that is discontinuous growth.
If growing point B starts to grow and growing point C also starts to grow then growing point C can also produce a scape and flower in the same season as growing point A flowered and that is also rebloom.
The AHS definition of rebloom -
"Reblooming, Recurrent, Remontant Having more than one cycle of flowering per year."
