CKwik is right, they regulate voltage and charge your devices accordingly just like a wall charger. Provide some info backing up why/how they damage phones if you suspect they do so.
While Mophie was really the first reputable name Aukey and Anker are good banks now. I've had both Anker and Aukey.
My first Anker 10000mah I wore out both usb ports on and since it was just a few days out of warranty Anker refused to replace it for me(by by Anker banks for me).
Bought an Aukey 16000mah, the first one swelled up and lasted less then one charge on my S8+ after about 6 months. I partly suspect it swelled up and went bad because my daughter was constantly using it to charge her iPad Mini 2 WHILE she used the iPad. Now I've got a 20000mah warranty replaced bank from Aukey, which my kids been banned from using at all, that's going strong.