4-way switch - common wires are not normal
It sounds like the voltage tester has issues.  There are other ways to identify the wires. 

Usually 3/4-way complexes are a mess (not least because the wire color does not correspond to the purpose in any way). But your 4-way switch makes this surprisingly simple: both pairs of messengers are on the red+black wires.  

So go to the remaining 3-ways.  Find the red+black pair that goes into the same cable: those are the messengers. The remaining wire is the always-hot or switched-hot.  

You will also note the messengers are on brass screws, and the always-hot or switched-hot is on the black screw.