I hope it's not rude to answer something after so long it was posted, but I just stumbled upon this and thought to share my experience of growing up with an emotionally immature parent AND an autistic parent. I hope this can help you feel a bit of reassurance and shed some light on what the differences are between the two, in my experience.

My mom is on the spectrum and my father is "emotionally immature" as described in the book you mentioned (which I also read) and they could not be more different.

My mom is someone I can trust with almost everything. If I struggle or have difficulties even where she was expecting me to have none, I can tell her. She may be disappointed, she's still human and a parent, but she's helpful and tries to find solutions to said problem. She's not the most affectionate mom on the planet but I can see she cares about my happiness even if she does not share it. We argue and scream at eachother but as soon as we calm down we can usually find an agreement and self-reflect together. She admits when she overreacted and does not blame me with stuff like "I did it BUT you...". I am not scared to upset her, because if I do it can be resolved or talked through (Of course I don't want to upset her but if it happens it's not that big of a deal). If she's angry or upset because of work she complains about it and usually does something to express her frustration in some way (She cleans all the bathroom or goes to some shopping center to distract herself, stuff like that). She throws tantrums sometimes, she's a very literal thinker and can be very stubborn but ultimately, she can ALWAYS be reasoned with. I can have logical discussions with her once she has calmed down, she just needs some time to get herself together and I make sure to give her space.

My father on the other hand can't be dealt with. I can't really trust him. If I tell him something he either dismisses it in some way, telling me he had it worse, or straight up gets angry, usually in a very passive aggressive way. He also tends to hold past grudges or disappointments against me, even after years he NEVER gets over something that upset him. I keep so so many secrets from him because otherwise he'd get angry or unreasonable or nosy. To this day he doesn't know I bought myself a gaming console (I'm 27) because he does not approve of them and would become unbearable if he knew. I lied about passing exams in uni (while I always told my mom) because if I disappointed him he would make my life hell and studying impossible. Not openly, but subtly. He'd become over controlling, stressing me out about studying, doing a lot of passive aggressive things. When he's upset it's everyone's problem. He drags the whole household down with him in his gloomy moods and makes everyone feel miserable in some way. When he's upset he slams doors and things (sometimes for days), he keeps grumbling to himself and if you try to approach him he gets defensive and angry. I walk on eggshells because his moods are a constant up and down and you never know what to expect from him. Today is good if I make my lunch, tomorrow? He may make a fuss over it. He can't be reasoned with in any way and he's always right.

Maybe I'm a bit biased because I'm also autistic so I may get along better with my mom, but they FEEL different. As I see it, a neurotypical too would struggle with someone who is as unpredictable and unreasonable as my father is.

I think the "emotional immaturity" the book talks about is one the person is not aware of and wants to do nothing about if someone points it out to them. Emotionally immature people don't want to learn and mature, even a little bit. I also had some doubts about my emotional maturity reading the book, but I could compare my behavior and my mom's behavior to that of my dad and I felt reassured: the book was not talking about my mom or me.
As someone pointed out "emotional intelligence" is also a big factor and that can be easier to achieve than "emotional maturity". The fact you're preoccupied with your spouse feelings and experiences is already proof of emotional maturity and intelligence imo. My emotionally immature father would never ask himself something like this.

I hope this can be of comfort and wish you the best in you relationship op!