Connect to Mac remotely using iOS, BTMM address and a VNC client
Not everyone can use the URL to connect. The connection is only successful when both parties in the connection are logged in to the same iCloud account. When you're accessing the URL on your Mac, you're logged in to iCloud so it works.

With iOS, I don't have experience trying to use a BTMM address there but I presume it is due to this. Try logging in to the same iCloud account on your iOS device, but if it doesn't work then it'll be because Apple don't expect you to be connecting over the BTMM address manually on iOS.