ajak told ikaris about the true meaning behind their mission because she feared herself falling out of line with what they were meant to accomplish. she had been dedicated to the emergence, to arishem for millenniums upon millenniums in many, many different galaxies. while she didn’t fully come around to not letting the emergence happen until modern day she had began questioning it as early as babylon. she could see that not only earth, but the people of earth were different. think about it. all ajak knew was the mission. to not let arishem down, as she quite literally says to him: i won’t let you down. the idea of going against the thing she was created to lead caused a multitude of turbulent emotions within her. informing ikaris of the mission meant she would have someone who she could rely on to keep her dedicated. to keep her steadfast. essentially, in line. and she thought that after millenniums of being able to live among people that ikaris, too, would have been swayed. it was a wrong judgment, of course. and then she paid the price of leading ikaris down the wrong path because the thing she had originally feared happened, the demise of her own devotion.