Are you obliged to exercise particular caution when turning right in this situation?

Yes, you must exercise special care for several reasons. Firstly, you are approaching an intersection with traffic lights. Secondly, and most importantly, the warning sign A-30 visible on the right with the supplementary plate "Wyjazd" (Exit) informs you of a place where emergency vehicles (e.g., ambulances) enter the road. You must be prepared for the possibility of having to give way to them.