No, it is not correct to use same utensils for handling raw and the cooked food.
Cooking raw food an meat with the same utensil, can cause the transmission of meat particles on the hamburger. The hamburger is not cooked in a similar manner to the meat, so, the meat particles on the hamburger may remain uncooked, and may be they are contaminated with some pathogen, which can harm our body system. Hence, it is important to use different utensils for handling raw food and cooked food.