Ok, here are the results.
First, I created another menu item that pops %AIR value. Both, after
starting airplane mode by HTC power button and by tasker task, popup
displays same result, %AIR = on
Then, in my profile, I replaced State>Airplane mode context with
state>variable value (%AIR) as you suggested. Now, my profile is
activated no matter what method I use for going to airplane mode!
So, I'm a noob, but this seems like a bug of Airplane mode detection
in State>Airplane mode context?