Unfortunately, it seems that in order to use her intuition, Reimu has to switch to incident-solving mode. She has already beaten up several innocent fairies. Thankfully though, she seems to have designated you as "support" and isn't attacking you. She is also ignoring everything you say, but that's hardly unusual.
You quickly arrive at Eientei, but Reimu doesn't seem to have switched off her incident-mode and appears to be set on marching in and beating everyone to a pulp.