This article shows the different settings that you can apply to generate the AMR mesh
When using Trimmed mesh, the AMR properties window has 3 options to set the Initial Mesh. This Initial Mesh property determines whether the octant depth from the initial trimmed cell mesh is recognized or ignored. By default, it is set to General.
If you generate the mesh using the Trimmed (HEX), the AMR can recognize the octant depths and try to keep to that division of cells.
For e.g. in the image below, if you use Trimmed (HEX) mesh as the option for Initial Mesh, the octant depth in the initial mesh in included in the refinement level.
However, the Trimmed (HEX) and AMR are not fully compatible and sometimes you might end up with AMR refinement which looks more skewed or has lower quality cells.
If you want to use Trimmed (HEX) option, then its good to check where the tricky cells are present in the solution that are difficult to refine. These are the cells usually with different octant depths but share a common face, they are most likely found on curvatures.
The default general option uses the standard mid-point subdivision of cells and hence it might give a better mesh in this case.
If you right-click on Solvers > Adaptive Mesh node and select Evaluate Refinement Status.
It creates a field function Adaption Refinement status. You can then create a threshold with this field function to check the bad cells. Set a value of 4 to check for unrefinable cells. If you find that a large amount of these cells are present in the area of interest, its better to use the General setting.
Alternatively, you can also use the Auto Detect option, which first checks if the mesh is compatible for Trimmed HEX, if not it ll use the General sub division.