Perhaps they discovered the true nature of time: and exist independantly
All biological process have a 'concept' of time - ie. even a stimulus and response within an individual, or evolution of an organism from one to a more adapted one.
So for your question how indeed could an organism exist truly without a 'concept' of time? We need to look at the underlying physics to see what time is to answer this.
Time is indeed a concept that seems easy to grasp. Past present future. Could one exist without the need for it, or for indeed a simple classical aspect like causality? How can an organism exist even without perceiving simple cause and effect (without the obvious alternate answer is it does not perceive at all)?
We need to have a look at the Quantum realm - Einstein, Feynman and Wheeler concluded that time at a 'quantum' level (ie. the scale of the very-small) is 'symmetric'. ie. It could flow in both directions. In particular this relates to electrons photons and particles that can interact with a historical particle, or is a 'reversed' particle flowing backwards in time. Feynman developed the infamous Feynman diagrams that demonstrate this concept - the 'time' axis flows both ways, and the diagrams for interactions could be 'rotated' for particles to travel in the 'time' axis, but also in the reverse of this axis. And interestingly, interactions could occur with no time - ie. perpendicular to a time axis meaning it exists both forever and in an instant.
This indicates time is not nearly as easy to comprehend as we used to think it was. Even Special and General Relativity bends our 'concept' of time - ie. time being different for observers travelling relative to each other or being closer to mass - our primitive standard 'concept' of time being simply a consistent past present and future is starting to look shaky indeed. Indeed, photons travel at light speed, and experience truly 'no time'. Even that classical truth is difficult for us to grasp, and it is demonstrably true.
So perhaps your aliens are smart, and have researched what time actually is: and they have made true discoveries that do not align with our primitive understanding of what time is, being the consistent march of regular intervals from past to present to future. Perhaps they 'evolved' beyond the limitations of time, and now exist on an axis of quantum existence that is perpendicular to the Feyman 'time' axis, or at least warps or bends it so much it no longer relates to our primitive inexorable march.
But how do they relate to each other? The answer is they already did, and did so in an instant, and will do so again. How do they perceive the world? Again, they already did, are doing it, and will do it forever, in an instant. Time is independent of them, like the humble photon that truly does not experience or perceive time, so do these creatures. They perceive the universe in an instant, and forever, and spatially everywhere.
How do we detect them, and interact with them? The same we catch and detect light, with detectors and materials that absorb them, collapse their wave function, to which we can see evidence of them, in 'our' time.