PWA not caching when refreshing in Airplane mode

I was following an Internet tutorial about progressive web apps, with the following examples (MWEs of the important files):

service-worker.js:

var dataCacheName = 'template-pwa';
var cacheName = 'template-pwa';
var filesToCache = [
  './',
 "./fonts",
 "./fonts/roboto",
 "./fonts/roboto/Roboto-Bold.woff",
 "./fonts/roboto/Roboto-Bold.woff2",
 "./images",
 "./images/icons",
 "./images/icons/icon-128x128.png",
 "./index.html",
 "./manifest.json",
 "./scripts",
 "./scripts/app.js",
 "./scripts/jquery-3.3.1.js",
 "./scripts/materialize.js",
 "./service-worker.js",
 "./styles",
 "./styles/materialize.css",
 "./styles/style.css"
];

self.addEventListener('install', function(e) {
  console.log('[ServiceWorker] Install');
  e.waitUntil(
    caches.open(cacheName).then(function(cache) {
      console.log('[ServiceWorker] Caching app shell');
      return cache.addAll(filesToCache);
    }).catch(reason => console.error(reason))
  );
});

self.addEventListener('activate', function(e) {
  console.log('[ServiceWorker] Activate');
  e.waitUntil(
    caches.keys().then(function(keyList) {
      return Promise.all(keyList.map(function(key) {
        if (key !== cacheName && key !== dataCacheName) {
          console.log('[ServiceWorker] Removing old cache', key);
          return caches.delete(key);
        }
      }));
    })
  );
  return self.clients.claim();
});

self.addEventListener('fetch', function(e) {
  console.log('[Service Worker] Fetch', e.request.url);
  e.respondWith(
    caches.match(e.request).then(function(response) {
      return response || fetch(e.request);
    })
  );
});

manifest.json:

{
  "name": "Template PWA",
  "short_name": "Template PWA",
  "icons": [{
    "src": "images/icons/icon-128x128.png",
      "sizes": "128x128",
      "type": "image/png"
    }, 
    }],
  "start_url": "./index.html",
  "display": "standalone",
  "background_color": "#3E4EB8",
  "theme_color": "#2F3BA2"
}

app.js:

(function() {
  'use strict';

  window.onload = function() {
    let message = localStorage.getItem("message") || 'Your message will display here';
    $('#message').html(message);
    $('#display').html(message);
  }

  $('#button').click(() => {
    console.log('click')
    let message = $('#message').val();
    console.log(message);
    $('#display').html(message);
    localStorage.setItem("message", message);
  });

  if ('serviceWorker' in navigator) {
    navigator.serviceWorker
             .register('./service-worker.js')
             .then(function() { console.log('Service Worker Registered'); });
  }
})();

When I run the PWA on my website, visit the PWA with my smartphone and add the PWA to my homescreen I can use it as expected. When I go offline (airplane mode), I can still use the PWA as expected. However, when I drag the screen down (refresh), the PWA displays "site cannot be reached".

Shouldn't a progressive web app be completely cached to be usable offline?