Not really. In ballroom tango the man's hand is further around the lady than in the waltz, foxtrot, etc. His fingertips will be on or across her spine. But his hand is also lower on her back as his forearm slopes down, so not really between her shoulder blades. In the US especially anyone can call themselves a professional, it does not mean they have much knowledge of what is actually important to physical mastery of a style of dance, or are necessarily making an effort to insure that what they do have is comprehensively passed on to their students. And every region has its own local variations which may be popular with casual dancers, alongside or seperate from more universal ideas which would be agreed upon by experts from both countries.
The goal should not be to control your partner but to communicate with her as subtly as possible. Relatively little activity in the right hand is needed, primarily your body moves your hand, so that she feels the movement of your body through your arms and hands (and possibly also directly from your body).Primarily you need to keep your hand in a stable correct place on her back, secondarily there are situations in which you will need to open your elbow a small amount so that the frame can "breathe" to give her a tiny bit more room. You can think of it as your hand going with her body, and your arm relaxing to allow the difference between her body and yours.
You should not be dipping partners without their previous consent. Ballroom "lines" are traditionally quite a bit different than dips.