foreign contigents in foreign lands to that contigent tend to remain loyal because basically they have their wifes and kids at home under the comand of the force that took them and at the same time since they are foreigners if they loose their military edge or show disunion the natives can rebel and take them out

the persians had a good road sistem and since the people that alexander took over where accostumed to law and order they just wellcomed the new masters and life continued (also the life continues part in persian meant that the maks and their allies had more food then they where normally accostumed to and also more wealth ) persia heartland was fairly easy the eastern borders with all the savages steppes and mountain warriors was trickier

also life back then was 20 km´s around your home (the distance you can travel in half a day on foot ) so for most people joining an expedicionary force wasn´t a bad career path compared to being a peasent! gave you a chance to rise in your station (or in the nobles case mantain your position before the new lords ) you got to see the world have acess to new beautifull women instead of marrying your cousin like you daddy arranged with his brother or with his own cousin ... (i mean whats new is always beautifull and we need to mix a bit more then just 20 km´s away from daddy´s farm ) so to replace soldiers wasn´t that hard aslong as you weren´t a racist xenophobic bastard (wich the makedonians where )

on that stand hannibal faced far worse against the romans then alexander because the persians where accostumed to arrive kick the hell out of whoever pissed them off and get back home in time for the new years festival and so fighting on their own land they where like wtf are we suposed to do ?