I have a Nokia Lumia 435 Dual sim running Windows 8.1 which I had upgraded from Windows 8.0. Everytime I try to upgrade it checks for upgrdaes and returns that the phone is already running the latest version or rather there are no new upgrades found. Yet I saw someone with phone just mine running windows 10, unfortunately he could not explain to me how he did it since someone did it for him. He just said I should be on wifi.
I am using W10M on lumia 535 and very happy with that. If you want to update on W10M you can easily use Upgrade Advisor app for updation since your phone is supported. See this link. Whoever you consulted was wrong at that spot that connecting to Wi-Fi forces upgrade. This app is the only official way through which you can upgraded. Without this app your phone will check the latest update of Windows phone 8.1. To upgrade your phone to W10M, you need to enable upgrade advisor's updates then you should go to check for updates. Just follow screen instructions and you'll be done. I have also attatched screenshots of my updation process for your ease. Hopefully it will help.