People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly timey wimey stuff...
Time differences only cause paradoxes if things are stuck on linear path from past to future. This is sort of like the many-worlds interpretation of quantum physics. Things can happen differently, and all the differences branch out into their own time line.
It really is kind of a neat way to avoid paradoxes altogether. It would still enable screwy stuff like meddling with a past. Let's say you took a trip from Earth to Delta Serpentis, and it turns out you're in 4,000 BCE (Earth time). If you could send a sub-light ship to Earth, you could introduce miraculous technology, pretend to be gods, and build some pyramids while you're at it just to screw with future generations. But it wouldn't really change the history of the GTVA because that history is already happened, and cannot be changed. You would massively change the future of the past-Earth that branches out to a new, unforeseen direction.
If that were the case I would expect them to have some sort of Prime Directive against this sort of stuff happening, but as we all know, starship commanders are known to ignore or circumvent the Prime Directive in certain circumstances.
The node network allows a stellar civilization like the GTVA to have continuity and fast communications, but it could mean the locations connected to the network belong to arbitrary time-lines. But, it doesn't necessarily preclude systems in the node network from being close to each other in the "galactic time" and you might still be able to effectively communicate with other system - like between Alpha Centauri and Earth - if the differences between the time-lines are small enough. In fact, all the time-lines should be reasonably close to each other, otherwise there would be noticeable differences in star locations and whatnot.
An interesting result of this kind of system would be that if a node is destabilized and then re-established by whatever means, it may connect to a different time line. Maybe ancient aliens have the ability to pick and choose which time line they want to connect to...