False. It is the case. Watch the video. I can send you another video of mine...but it would look just like that. It has nothing to do with the vehicle's computer. I have a factory rear E-locker and an add-on front E-locker (wired direct like yours), and they both require a rotation to engage. There is no lag in the switch light coming on...and there is no lag in the coil being energized...but there is a lag inside the diff before it is truly locked. Sometimes you can hear the coil "click"...sometimes you can't. But the "click" is just the coil and it does not mean the diff is locked. It still takes a full turn to be locked. The notion of "instant lock" when you press the button, is not possible. I think many H3 owners don't realize this, and thats why there are so many issues with the pins inside the factory units getting rounded off. You can't just push the button and pour the pedal to it.
Also when you change direction...the Eaton will dis-engage. This doesn't mean it shuts-off at the switch...the coil is still energized. It just means you have have un-spun it, and you will once again need to spin it back the other way one full turn, to be truly locked. The intermediate time between pushing the button and spinning it to fully locked...is where you can do some damage. So anytime you push the button (or back-up)...make sure you allow ten feet of travel to get the diff fully locked. Its probably less than one full turn, if you are rolling in a straight line. But if you are in the middle of a turn, (with the wheels traveling at different speeds)..it could take up to a full rotation for the pins to align. Obviously, we rarely have room to travel 10-feet to engage a locker...but keep this in mind when you are wheeling an Eaton.
Many ultra-hard-core Jeepers frown on the Eaton E for this reason. If you want to stand your locked rig on its bumper, rev it back & forth between forward and reverse, all the while spinnin & grinnin...you need the ARB or the OX. Crash-locking an Eaton will guarantee an early failure.