Should I replace particle board underlayment before installing ceramic tile?
Your underlayment is particle board and is not suitable for ceramic tile. Most tile mortars specifically disallow bonding to particle board. 

Replace the underlayment with 1/2" cement board or 1/2" (or thicker) CDX plywood, or overlay 1/4" cement board if finished height isn't a concern. Either option should be screwed down thoroughly using corrosion-resistant screws in an appropriate grid pattern, such as 8" by 8".