Yep this is actually part of the 5 test to see wether he is Worthy enough to save kuro later on (among the other test is facing megiddo, that huge ahh dragon which i forgor the name, etc). The test is supposed to measure how calm he is at the time of crisis iirc (because damn boy he does need it when the time come for Kaito vs Kuro). But actually, Alice herself actually had no intention to reveal herself after saving kaito, she intended to save him as (i forgor either as a costume or as phantasmal king). but prior to that alice felt like kaito is similar to now her deceased best friends with the way he throwing tsukkomi everytime alice purposely trying to play stupid (her name is iris and she is from the same world as alice (not earth tho), and no, iris and isis is a different person, but later on iris become death king subordinate waaayyyy later on). Looking at the way she betrayed, she just know it that kaito wouldn't forgive her and that's fine by her since she is about to scrap alice persona anyway, but turns out he did, with that "don't spend your money uselessly" at the end, just like how iris would react at their former world toward alice. Hence her reason for reveal after saving him. This is actually also a turning point for alice as well since this is also the moment where she started growing affection to kaito (they still remained at friend status, atleast until eden/makina, earth god from kaito previous world kidnap him). By then she realize how irreplaceable kaito is and how helpless she is when it matter the most. After saving him, having a mental breakdown and telling all her past stories (or is it?

), she come to confess to Kaito