Will the Visa get issued within two months of applying for extension

I’m currently doing my master’s in Japan, and I’ll be starting my PhD soon. I can only apply for my own visa extension after I receive my official PhD offer letter, which should arrive in the last week of September.

My husband is here on a dependent visa, but his visa will expire at the same time. Once I get the PhD offer, both of us plan to apply for visa extensions together.

I’ve heard that when you apply for an extension, immigration gives a temporary stamp on the back of your residence card that lets you stay in Japan for about 2 more months while the application is processed.

My question is: if we apply together at the end of September, will we usually get the new visas before those 2 months are over? Or are there cases where it can take longer, meaning we might have to leave Japan while waiting?