Imoen's second ability triggers only if you have the initiative as your end step begins. If the ability does trigger, it will check if you have the initiative again as it tries to resolve. If you don't still have the initiative at that time, the ability won't resolve and none of its effects will happen. Notably, if you don't have the initiative as your end step begins but you have completed a dungeon, the ability won't trigger and you won't draw any cards.