Yes, non-citizens get utility bills, too, but they have to also show up on the list of registered voters. Of course, they can claim to be registered if they don't show up on the list, and they would be given provisional ballots.
But in any case, if people throw their utility bills in the garbage, I could get my hands on someone else's utility bill just by doing some dumpster diving or rooting through someone's garbage can, if I were so inclined.
So they register by mail (as I did), checking the box that says they are a legal citizen. They go to the polls with a utility bill (as I did because I haven't changed my street address on my license since the PO box remains the same) and are permitted to vote. No evidence of citizenship is necessary in PA, that's for sure. That may become an issue in Hazleton, but it has to be an issue in those states with a high number of illegals, unless they have laws on voting stricter than PA.