Yes, it is true. On the US server I have five cities in my account. When I purchase diamonds, it is on
my account, not
the city I was in when I made the purchase. Otherwise, why bother? I'm not going to make separate payments for each city. If you're gone for x amount of time, players sometimes get emails offering diamonds upon their return. Those diamonds are in your account and are shared between your cities as well.
Seems like this would seriously lend itself to abuse
The new city is in your account that already exists. It's the same as if you started the game in Arendyll as a Human, then decide you don't want to be Human, so you start an Elven city in Felyndral, build it up, then decide you actually
do want to build up that Human city, and start playing that one again. Any diamonds that show on your header as available to you in Felyndral are there in the old city in Arendyll because it's one account, it's not like you made two separate accounts intending to push one with the other. You can't share diamonds between accounts anyway...