The message means that your solution may be on the verge of diverging, so Fluent is introducing some mechanisms to stabilize it.
Reducing the time scale factor is another way to help with stability at the cost of convergence rate. If you're able to get a solution within an acceptable amount of computation time by reducing the time scale factor, then you can work with that.
But no, this is not "typical" when increasing the number of cells, unless the changes in the mesh result in worse mesh quality.
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