Depending somewhat on the airline, J class usually means FULL fare refundable business class. However, a travel agent might be selling a bulk or consolidator fare that isn't refundable/changeable.

Is there any chance your "travel agent" is really a mileage broker? Often they will seemingly make a reservation but postpone purchasing a ticket until a low or saver award ticket becomes available, which might be never. In this case, even if your have tickets that aren't cancelled by the "travel agent", you could be stranded if the airline discovers that your ticket used purchased or stolen miles.