It's gotten so I can no longer read posts on my iPhone. I click on links in the email and immediately after I start reading it opens new windows and my App Store where it wants me to download Candy Crush or Loovo or some other app.

It doesn't happen on other pages or when I use my PC. Why does Thaivisa not want me to read articles in my phone?

It looks like some malware got installed on your phone.

Something is adding page calls to your browser.

Sounds like some rogue javascript is being delivered to your device via your internet connection.

Make sure your device is using authorized DNS Servers. If your Internet router has been compromised or hacked, it could be set to route all your traffic to third-party servers that can/will edit non-https pages and scripts enroute, replacing page elements or scripts to deliver whatever they want.

Your device should report that it's using DNS Servers from your ISP, Google, or those you have manually entered.

Th strange thing is, it doesn't happen when I'm on my own network, only on 4G. It's happened both on a Thai network DTAC, and a European carrier T-mobile and only when I click on Thaivisa email links.

Probably an intermediate proxy server or gateway doing edit/injection on the google ad scripts while they are in-transit to serve additional pages.

Usually I would recommend switching to HTTPS, but ThaiVisa doesn't offer that. So employing VPN would be the only way to prevent script injection in-transit.