I'm sorry for your loss. But don't panic or beat yourself up, It doesn't sound like there were many things (if any!) that you could have done better or differently.
First off, finches and parakeets aren't that closely related. Not that many fatal, virals in common with each other. They didn't share bowls for food, they didn't come from same place, and they didn't go to the same place. Sounds like a very limited exposure to each other. I wouldn't rush to diagnose Proventricular Dilatation Syndrome (PDS) without having a vet confirm it. PDS is usually found in psitticines, and although it's possible it can occur in passerines, I couldn't find any literature that included small finches in the list of species susceptible to it (One resource was here with the Int'l Aviculturalists Soc.: http://www.mecca.org/~rporter/PARROTS/pds.html
). There is a syndrome of finches that causes them to waste away but I believe that there are a number of causes for that, and it may not be viral (ie non-contagious). (Here is a source on that: http://www.lostmymarblz.com/fl-health-goinglight.htm
The fact that they both had the same symptoms at the same time and died the same night is puzzling. I guess it's possible they were exposed to something at the same time and it had an identical incubation period in each bird, but in reality that rarely happens. If it did, it probably happened before you got the birds.
I guess a stress event is a possibility also (you described a long car trip, although I have traveled many times with birds in a car and no bad after effects), but I'd expect something like a cat knocking their cage off a table. Something would have to be pretty traumatic to affect them that strongly, and it would have to be fairly recent.
In my mind, the only thing that comes close to explaining a double death like that would possibly be a quick acting, airborne toxin of some kind. Carbon Monoxide is one, there is also a colorless oderless gas which is given off by heating some items with non-stick coatings. Did you do any cooking the night these guys crashed? Was there a space heater of any kind running?
You probably already know that finches have super fast metabolisms, that they hide their symptoms until the last possible moment, and when their health crashes, there is usually nothing you can do about it ...they go down quickly. Nothing you could have done would have changed this. Even if you had taken them to the vet at the first sign of symptoms, it might have already been too late. So don't kick yourself over it.
To sum all this up, I'd keep an eye on the parakeet, but not worry overly much. I think it's very unlikely you did anything to harm it by merely hanging its cage next to the finch cage. You will probably never know what happened to them. I think it sounds like you did your best for them, and that's all that can be expected of anyone.