Should I rinse AJAX spray n wipe after use?

I sprayed my baby's plastic mat with Ajax spray n wipe and when I use this product I never rinse it with water - I just wipe it until it's dry, I do what the bottle tells me to do - spray and then wipe. My wife insists and demands that I need to rinse it thoroughly with water because she's scared our 7 month old baby will ingest some of the chemicals and have some long term effects. The bottle says no need to rinse...