That is fascinating. The parakeets are basically providing an early warning system, and the dogs have figured out enough of their "language" to subscribe to it.
My in-laws had a Chihuahua as the alert dog and a Doberman as the guard dog. Yip yip yip WOOF WOOF WOOF. Took the Dobie on a lot of walks in natural areas where sketchy people were around. Funny enough, nobody tries anything when you have an 85-lb/40 kg dog. They saw me put her on a leash when I saw them and they knew I could just drop it.
There's a more complicated example with fork-tailed drongos and meerkats. The drongos can mimic the meerkat alarm calls in order to panic them at strategic moments (and swoop in to take food), along with a high percentage of genuinely helpful alarm calls to keep them malleable.