Never Used Globe Airboost, but what I read in some forums. Airboost is manufactured by NEC and it is a Femtocell Access Point (FAP) It needs internet connection to activate but sometimes it depends on how the provider activates the device. NEC made this a plug and play system but not quite sure how Globe design the activation process .Like At&t they have a web activation and it requires to input the location for GPS . Probably Globe uses SIM card activation since Globe airbooster has a SIM Slot .I would say there is something wrong with the installation or how they set it up. Femtocell standard architecture are WCDMA, CDMA2000, LTE and WiMAX. .
I would suggest to call back the installer and make sure the set up is correct not just saying it's depend on ISP connection while your PLDT fiber line is working fine.
Hope this helps