My experience is that participating in the Find My network is not the problem, the problem only occurred to me when the AirTag was added to my account. If I had to make a guess, I would say this is caused by the anti-stalking measures where the iPhone regularly needs to check whether the AirTag is around. This is needed because if the AirTag is around a device associated with the same Apple ID then other devices moving with it do not notify their owners.