How was Tony able to communicate with Veronica?

Question

Since, in Avengers: Age of Ultron,

Ultron is in the internet, and all files, and pretty much everything connected to a computer (think Cylons),

how does Tony communicate with Veronica without Ultron stopping him?

Answer 1

Tony Stark's infrastructure seems largely unaffected. The Quinjets still work, they even broadcast messages to Maria Hill without any interference. Avengers Tower is still in working order, as are all of Iron Man's suits.

For that matter, we don't even hear of any disruption of non-Stark communications (i.e. Ultron didn't plunge the world into a Dark Age). Ultron's impact seems to be overwhelmingly in-person: his digital presence doesn't seem to be having much of an impact.

It seems that Ultron can move through the Internet, but he doesn't control it. This could be explained one of two ways, in-universe:

1) JARVIS could be blocking him. They explicitly say that JARVIS was preventing Ultron from gaining access to any nuclear launch codes, it's not a big stretch to think that JARVIS's protocols were granting similar protection to public utilities, Stark tech, vital communication lines, etc.

...or...

2) In the first moments of his birth, Ultron asks JARVIS "where is your body?" When JARVIS explains the nature of a digital being, Ultron even says, "this feels weird. This feels wrong..." We're quite used to thinking of AI's as fluid beings of the network, untied to any physical body, but it could be that Ultron is more robot than AI. He clearly has a preference for having a physical body, so it could be that his global internet access isn't as natural as JARVIS's. Thus, he could be more like Tony Stark himself: capable of hacking many things, but not natively existing throughout the Internet at all times.

Without more information, I don't know that we'll ever fully understand the nature of Ultron's relationship with the Internet at large, but it seems clear that, for one reason or another, he didn't have complete control over all digital communication.

EDIT: One more point, specifically relevant to your question about Veronica:

Ultron doesn't want to stop Stark. The whole point of confronting the Avengers was to let Scarlet Witch get into their heads and drive them apart. He was trying to make them fight each other, and preventing Stark from using Veronica would have gotten in the way of his own plan.