Honestly I think the atmosphere around their matches is nothing special. After all Leverkusen is and will be a suburb club that's lucky it's affiliated with a huge corporation. And yes, while of course everyone wants to beat them, after the match it's mostly "well, nobody else could beat them, so no shame in not doing it today".
Actually I think the completely dominant league win lead to the general mood being more disinterested then most would have expected. Everyone thought that some day there finally has to be a team that grabs the title from Bayern's claws in an epic battle. Instead Leverkusen has been mostly cruising through the season and it has been more boring than most of Bayern's recent title winning years
Still everybody is happy that Bayern's streak ends.