I have the exact same problem. I changed my tagline, like two weeks ago, but the old one still shows in the header image. I typed the new tagline in both Customize > Site identity and in Setting > General > Tagline. I also deactivated all plugins with no succes and I checked it on both Firefox and Explorer, but the problem stays.
The weird thing though is that the correct tagline shows up in my favicon, so it has changed there.
Did you solve your problem Virgilio, and if yes, could you tell me how?
Thanks a lot,
Theone
Website: www.theonetekst.nl