Taken from the KS comment section:
To answer your question, if you were the second player in a two player game (and thus the oldest Einstein), the game would end after your turn as you described it. Basically, the end game triggers are (a) someone draws their last inspiration card into their hand, (b) someone reveals the last major theory, or (c) someone only has two types of idea tiles left. When that happens, play for that round continues through the oldest Einstein (so everyone has the same number of turns) and then the game is over. In you case, drawing your last inspiration card as the oldest Einstein would end the game after your turn is complete as you suggest. Score the points and determine the winner!