Are welcome swallows native birds?

Are welcome swallows native birds?

Our welcome swallows came from Australia, where they migrate

between mainland Australia and Tasmania. It was probably
when they were migrating that they got caught in a storm which
blew them towards New Zealand. Some of them made it to Northland in the 1950s.
They nested there and raised chicks. As their numbers increased, they
spread south. Now they can be found all over New Zealand.
Welcome swallows are native birds because they arrived here
by themselves. 

On the other hand, sparrows and blackbirds are introduced birds because people them to New Zealand.