I maintain that Alastor is not stuck in the past. Alastor has chosen and embraced timelessness, aka, "I use the technology that is convenient to me, dress the way I like and talk the way I enjoy". Alastor is simply not chasing modernity, and IMHO by sheer virtue of this is a lot more "modern" than Vox with his obsession with being new, latest and fashionable. Every single look and act Vox puts on ends up dated in two years, while Alastor from the early 30s is exactly as contemporary as Alastor today. Vox needs Velvette to manage a new medium for him, Alastor edits a commercial and hijacks a VoxTek speaker without blinking an eye. Alastor is unchanging because radio is a fundamental technology for all long-distance wireless communication and a well-tailored suit will never not look good, Vox changes himself with every latest fad.
Alastor's manners might be vaguely "old timey", but he is, in practice, always exactly as polite as he wants to be to each individual person, no matter how time goes on, because his manners are based in fundamental respect towards the people he's talking to. Vox stumbles into 50s guy microaggressions approximately every other interaction, because to him other people are mostly not real.
This might or might not be related, in my opinion, to the fact that Alastor died in his 30s (still young and ready to embrace the world's changes, even as he has already acquired his personal idiosyncrasy), while Vox died in his 50s (calcified in his opinions and slowly losing the capability to learn new things).
And yet Vox will always, always call Alastor "old man" (in between "twink" lol). Because Alastor, to Vox, seems like he embodies Vox's fear of being irrelevant, of falling behind, of failing to embrace the changing world and keep up and stay forever young and the hottest thing around. And Vox cannot understand why Alastor does not appear to be bothered by this.
And Alastor will always look down on Vox's pursuit of novelty, recognizing it for the desperation that it is.
(The degree to which Alastor might be sympathetic towards said desperation varies based on your personal radiostatic headcanons lol)