Is it a wire escutcheon? If it's a modern reproduction, it's possibly an extrusion with parallel sides which doesn't make your job of fitting it any easier (lightly file a chamfer around the periphery of what will be the back of the escutcheon to assist entry into the wood). If it's a quality cast reproduction, then its sides will likely be tapered.
Either way, measure the major and minor diameters (if round-bottomed, or the width if square-bottomed) and drill appropriate (slightly undersize) holes in the spice box. If this is your first attempt, I would recommend a dummy run on a scrap of the same timber. Hammer the escutcheon in flush with the wood surface (taking care not to leave an indent in the wood). The escutcheon can be driven out from the reverse with a suitable drift, so practice as many times as you need to.