Daylilies flower by producing a fan of leaves and then a scape from (usually) the centre of that fan. The reason that it is usually from the centre of the fan is because the fan has reached maturity when it produces its scape and it is basically complete. The fan finishes its cycle of growth at around the same time it develops its scape by producing a replacement fan - a baby fan. The baby fan is usually either one side or the other of the scape and right next to it. The new baby fan can grow very rapidly because the crown is mature and can help it by providing it with some of its stored nutrients so that it gets a good and quick start to its growth. Depending on how quickly the new baby fan grows it may reach its mature size in the same growing season or the next season (or even later seasons). If it reaches its mature size in the same growing season it may produce its own scape and flower. That is rebloom. I would not consider that rebloom from fan increase as the previous fan is replaced by the new fan so there still would only be one fan. How quickly the new fan grows (how many leaves it makes before it makes a scape) may depend on its growing conditions (we do not have any information that I know of about that).
Sometimes the mature fan produces two new baby fans. One of those fans would be increase since instead of one fan there now would be two fans. I do not know if there is any information about whether one or both of those fans can flower in the same growing season and produce rebloom.
