Is this a correct installation for a doorbell transformer
The transformer is in a box so it’s not horrible but normally a doorbell transformer is mounted outside the box , the 120v connections made inside and the low voltage connections made outside the box. 
In this case both high and low voltage are in the same compartment , that would not fly in my jurisdiction with out a non conductive shield (plastic insulator dividing the hv / lv. Unless the MFG instructions directed it done that way.