The Time Stone is being worn by the Ancient One when Banner goes to find the Time Stone so we can boil this down to is the Ancient One in the wrong place instead of the Time Stone. The answer is simply probably not.
The sorcerers can travel to anywhere they want through a variety of means, the Sanctum Santorums are connected and they could always just use a Sling Ring to travel to where they want to anyway. So we've established that it's perfectly possible that the sorcerers can travel between sanctums.
That door leads to the Hong Kong Sanctum, that door to the New York Sanctum. That one, to the London Sanctum.
However, why would the Ancient One be in New York. Beyond the mundane explanation of she isn't the protector of any of the specific sanctums, under my understanding, so probably travels between them anyway we could assume she was there in case she needed to protect the sanctum during the attack.
The Sanctums protect the world, and we sorcerers protect the Sanctums.
Other-dimensional beings that threaten our universe.
Potentially she didn't know what was attacking New York in 2012 and so was there just in case but when she saw what it was, stopped paying it much mind.