We have tested current Robo Gallery version on multiply Android and iOS devices during last hour and I can confirm one more time that our gallery work properly on iOS and Android. For iOS testing we have used next devices: iPhone 4, iPhone 5, iPhone 7, iPhone 8, iPhone X and iPad. There’s no problem with gallery navigation or load of the gallery images. All thumbnails of the gallery images load properly with required animation. No delays. Lightbox of the gallery work properly on every device. We used for testing our demo gallery locations. You can open it and you’ll see that everything work properly.
Another important point. When I try to open your links, I mean link on your test and production server I can’t see gallery there at all. Looks like gallery completely turned off on both links.
Our gallery have cache engine which create cache of every gallery if this option enabled. Maybe, you turned off gallery someway and on other devices you see some cached pages, but on mobile devices you didn’t open this gallery before and as result you don’t see any gallery pages.
Please post more details to make us able to help you. For now I can’t see page with gallery which one do not work on iPhone.