That's because there's no real way for them to know you moved a number. Nobody knows you moved the number except the two companies involved. So, unless they had direct access to the customer records of each telco, they can only guess by the original owner.
That can't be true. If a number was ported from Carrier X to Carrier Y and someone makes a call originating from carrier Z, I am pretty sure carrier X is not involved any more in the routing of the call, which means that carrier Z has some way to figure out which carrier to route to (Y in this case). So it's not just those two companies involved.
At least in India, there exists a central database of ported numbers which every carrier uses to do the routing.
This is not true at all. I can give you the current provider of a number that had been ported and my data will reflect a new port within minutes of it taking effect. Oh, and it's an order of magnitude cheaper than what Twilio is charging for this... I couldn't tell you why Twilio's implementation is out of date and so expensive.