I have the same problem with my Sony Vaio Pro 13 and the iPhone 5S hotspot not working. The hotspot works fine with my MacBook Pro. Also, The Sony Vaio worked fine with my Previous phone hotspot-a Galaxy 4S. I've spent sever hours on the support line with Sony and could not fix the problem. I read one of the replies about the problem only occurring when the laptop was not plugged in on battery. Sure enough this was my problem to.
I finally found a fix. I relates to the power setting.
Go to control panel
Hardware and sound
Power Options
Edit plan settings
Change advance power settings
Go to Wireless adapter settings
Power saving mode
Go to On Battery and change it to Maximum Performance
Hit Apply and you are good to go.
I struggled with this for a long time since getting my iPhone. I hope this helps someone else.