You mentioned in your edit that you used a chromatic tuner. An E will register as an E even if its the wrong E on the chromatic setting. My tuner has a function called "G" which shows you the string number. So that when tuning the E for sixth string, unless it says 6E you have the wrong E.
Gary
[Epiphone Les Paul Standard Plus Top Pro (2), Fender Player Stratocaster (2), Fender Player Telecaster (2), Squire CV 60's Stratocaster, Hamer Ecotone, Yamaha APX600 (2), Epiphone ES-339, GTX-100 (2), Spark 40 (2), Spark Mini.]