Sayadaw U Tejaniya's method emphasizes observing the state of the mind over the specific object it's observing, but it includes both.
The quality of the observing mind is of primary importance:

• Mind States are Key: His main teaching focuses on recognizing the attitude or state of mind that is present while observing an object. This includes noticing if the mind is relaxed, tense, curious, bored, greedy, averse, wanting to control, etc. He states, "The object of attention is not really important; the observing mind that is working in the background to be aware is of real importance."
• The Object is Known: You are certainly aware of what the mind is observing (the object)—whether it's a sound, a bodily sensation, a thought, or an emotion. This object is what triggers the mind state. For example, the mind notices the object (pain in the knee) and then an accompanying mind state arises (aversion or wanting the pain to go away).
• The Focus is on the Relationship: The wisdom in this practice comes from seeing the defilements (greed, aversion, delusion) in the mind's relationship to the object. You don't try to get rid of the object (like the pain), you simply observe the state of mind reacting to it.

In short, you are aware of the object of attention, but you are primarily interested in the attitude or state of the mind that is doing the knowing or reacting to that object. This is a practice often referred to as mindfulness of mind or cittānupassanā.