I do not know this circuit, but you very well could have smoked your undersized resistor. And, if it was carbon composition, it would tend to be pretty smoky, particularly if it scorched a printed circuit board while it was destroying itself.
Your Ohmmeter will tell you for sure, if it is not readily apparent. Some de-soldering braid will help you remove it, if it is indeed mounted on a PCB. And, two 560 Ohm, 1/2 Watts in parallel would net you 280 Ohms with 1 Watt of dissipation. But, again, I don't know the circuit to be able to tell you if the extra ten Ohms is acceptable.