By the looks of things, the army does things a little differently than the AF or Navy. We have fanout/recall that can be activated at any time, by pretty much anybody above you in your chain of command. Sometimes it is just testing out the fanout to see how quick pers can get to work. Sometimes there is a legitimate reason for pers to be recalled to work.
As for a cell phone, no they are not required. If you are going away out of the area you will have to submit a leave pass, with a contact number you can be reached at. (hotel phone number, friend's house number etc) If you are the on duty pers you would be temp. issued a cellphone/pager.
And if you want to stand in front of your WO or Sargeant-Major, sure go ahead and not answer your phone. But like I said, things are different in the other 2 elements.