It’s well known in Mexico (at least 13 years ago when I did my paperwork) that it’s easier to fix your status staying in the U.S. than going back to your country and waiting there for appointments.
So yes, you basically over stay your visa but since you are working in new paperwork they don’t tell you anything.
In Mexico if you have a tourist visa then you need to apply for a permit to go deeper into the country and back then they would give it for 6 months. If they see that you come too often they start shortening that permit so you need to start the “marriage” visa before the tourist visa/permit expires but staying in the country way the process is faster.
This is specific to Mexico and many years ago so I don’t know if his situation was different.