There's quite a bit of discussion about this cheap penetrant, this one may be related to your concerns:
https://www.bikeforums.net/bicycle-m...urt-tires.html
I would wash the whole bike with your fave bike soap, and then avoid using WD40 at all.
All rust inhibitors don't work if dirt is left there to keep things moist and mushy.
Regularly washing a bike and having it lazily drip-dry will be more effective.
Despite how crappy WD40 is, it will penetrate when left over long periods of time, and you don't want any of it to mix with any lube, especially in the BB.