Is there something I don't get, are private lessons a routinary thing in ballroom?
Yes, private lessons are a routine thing in the ballroom world. How routine depends on your goals. If you're only interested in surviving social dancing, then you can probably wait a bit. If you want to become an adept or expert social dancer, or have any interest in competition, you should always include a mix of private lessons with your group classes, at whatever rate your resources allow, while keeping in mind that resources include not only money but the time for the lessons and to practice them.
While salsa does have a great deal of technique in it, much of the technique in ballroom is subtler. If you do only group classes not only will you miss out on much of that technique, but you can build in bad habits that you must later spend a good deal of time and money correcting. Investing in private lessons early with a good teacher, along with diligent practice of what you work on in those lessons, is the best way to prevent this.
In salsa they would function as a way to improve details when you already have a good command of the basic step.
That's one of the functions private lessons can have, but not the only function. In my article,
"Getting the Most From Your Private Lessons," I talk about making sure you have a goal when you walk into a lesson. If you've been dancing salsa for awhile and have had the pleasure of learning from high quality teachers, I'm sure you're aware that a good teacher can spend an hour teaching a step you already know, even the basic step, and make it not only fun and interesting but useful and improve the entire dance. Because of the aforementioned subtleties in ballroom, you will experience this to an even greater degree. Based on my own experience, it's not uncommon for me after I learn a new technique to ask my instructors to go over the entire beginner syllabus with me to make sure I'm including that technique in all my old steps - especially the basic!
My recommendation, especially for beginners, is to spend their private lessons going over the material covered in the group classes. This ensures not only that you'll remember the material each week, but will move you toward mastery of the material.
Basically, I think privates are a waste of time and money at this point.
I hesitate to bring this up as I can almost guarantee I'm going to offend some salseros out there, but I suspect that this has a lot to do with having had bad teachers in the past. Unfortunately for the salsa world, due to the nature of the community it is quite possible for an adept dancer to excel and develop a reputation as an excellent dancer without being completely trained. Consequently, many of the salsa teachers out there are people who are good dancers but A) don't know how to teach and B) only have limited experience with their partner's role. Lessons with these teachers are, by and large, a waste of money outside of a few specific areas (these teachers tend to be very good at choreography, club styling, and having an elaborate repertoire of moves, for example). Compare this with a master salsa teacher who can not only teach patterns - and has as much to say to men as he does to women, and vice versa - but can also teach technique, arm styling, hip motion, adjustments for a social floor vs. competitive floor, put together sequences for social dancing or competition, choreogrpahy performance, and demonstrate everything superbly. There is no comparisson!
Finally, keep in mind that your partner has more experience with ballroom than you do. Your experience with salsa is quite valuable and will make the learning process for ballroom easier, as well as give you the experience to provide critical feedback and opinions on how the lessons are progressing, but remember to give appropriate weight to her opinion. I'd suggest scheduling a single private lesson with an instructor before comitting one way or another. From there you can decide how much you need from the lessons, you can examine your time and budget, and decide how you want to progress.
Good luck and welcome to the world of ballroom!