I use the next hack for this via Reflection
public static void hackTooltipStartTiming(Tooltip tooltip) {
try {
Field fieldBehavior = tooltip.getClass().getDeclaredField("BEHAVIOR");
fieldBehavior.setAccessible(true);
Object objBehavior = fieldBehavior.get(tooltip);
Field fieldTimer = objBehavior.getClass().getDeclaredField("activationTimer");
fieldTimer.setAccessible(true);
Timeline objTimer = (Timeline) fieldTimer.get(objBehavior);
objTimer.getKeyFrames().clear();
objTimer.getKeyFrames().add(new KeyFrame(new Duration(250)));
} catch (Exception e) {
e.printStackTrace();
}
}