Alexander's decision to send the bulk of his army down south was taken primarily based on reading the various missives Perseus sent Lord Ponticus.
Those had proved to be quite insightful for Alexander, as they detailed various internal secrets of the country.
For instance, he could indeed confirm that the 10,000 reinforcements so touted by Lady Felicia indeed exist.
He also learned of Tibias' dire financial strains, the various factional rivalries, the most prominent one being between Mithriditus and Lord Theony, the king's thoughts on his son, much interesting but not useful palace intrigue, and most importantly of all, the country's grievous manpower shortage.
And upon reading it, as well as Lapitus informing that the most force the capital would be able to master was perhaps another further 10,000, alongside the already raised 10,000, Alexander saw no reason to dally and give the enemy any chance to breathe.