Meditation has many techniques. Similar to how people have many different motivations and programs when they have a regular gym practice.
Strength is different to agility is different to flexibility.
In more formal traditions the focus on breath (or similar) is to develop concentration/samatha/samadhi.
The focus on sensations is the insight/vipassana component, and often this is where the tension bubbles up to the surface. Keeping calm (equanimous) during this process can indeed be non-trivial!
It sounds like you have come to a practice very similar to a lot of the Burmese traditions of insight meditation, which is quite fascinating.