Space is big.
Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.
Douglas Adams "The Hitchhikers Guide to the Galaxy"
We like to think that radio waves we send out can be picked up by another civilisation, but this is just a huge comforting lie. Distance to Alpha Centauri system is about 4.37 light years. Radio signals lose power as a square of distance. For comparison, as of last year, Voyager 1 is 137 AU away from Earth (1 ly is about 63000 AU).
According to this answer power of about 20 kW is needed to communicate with Voyager probes. Knowing that, we can estimate that since Alpha Centauri is about 2000 times further away, communicating with it would require 4000000 more power, for a total requirement of about 81 GW (Giga-Watts). And that's using large focused antennae. Radio and TV transmissions dissipate into noise much sooner, I doubt they are detectable beyond Pluto's orbit.
Basically, detecting random radio transmissions is a pipe dream. You can have interstellar radio communications only if you use massive antennae, pumping terawatts directly at other systems. Unless you actually know there is someone to talk to, it's rather pointless, even without considering light-speed communication lag.
Because of that, you can have two civilisations inhabit neighbouring stars without ever finding out about each other.
Only real chance is if their probes, scout or colony ships happen to run into each other in some system. If you want to eliminate this risk, you simply need to make them completely different in terms of biology.
Through observation of other stars, including planetary transition effects, we have a pretty good idea where to find rocky planets like Earth, located in local goldilocks zone. There is little reason to visit systems lacking such planets, because those are the ones which could possibly be seeded with Earth-like biosphere and as such, are the most interesting for us. Simply give aliens vastly different requirements, and they will not bother visiting systems targeted by humans. This can go on for a very long time, with both civilisations being entirely spatially intertwined without ever learning of the others.
Until they happen upon system having planets preferred by both...