Both my husband and I have Verizon and have paid to add the international plan for our trip to South Africa. He is on a separate plan with his sibling. However on arriving in Germany and now South Africa. My phone works (I have an iPhone 6) and his says no service at all times (he has an iPhone 6+). He has restarted his phone twice. Is there something else he needs to do to get service here. This is very frustrating.
I would try to go into settings>general>network (or something of the sort) and reset the network settings. Also check the network settings in general. I don't think the iPhone has a network mode, but look for that - androids have a Global setting which is what you'd want it to set too. You can also look under your phone for more ideas to give him and also see what your settings are set to and try to compare.
Was the plan actually added? Confirm with My Verizon. Also make sure Roaming is on in Cellular settings. Reset network settings and turn off fully and restart are also good steps.
I recently had thesame problem travelling in Chile. Most of the time, even when there were local networks available and the reception was excellent, as shown at the top of my Pixel 3, the phone did not connect and I was unable to text or access the internet except while in WiFi. Calls to tech support, even level 2, were no help and when I returned to the US and called again, tech support said they were unable to help me. Even at $10/day, this is a ripoff and it lowered the enjoyment of my trip. I've heard that AT&T has better international calling connectivity.