What elements in Tomato and Spinach make them cook quickly when cooked together?
The table salt is probably irrelevant to why the veges cook down quickly, although it does cause veges to sweat, it may leach the moisture out of the tomato and spinach faster than if you didn't add it but I think heat would be the main variable. Also do you stir the food more when you add the salt than if you didn't? 

Most organisms have a ratio of about 《80% water, spinach and tomatoe may have a high water content and also contain oils and other volatile components that are released when heated so when you heat / cook them the water and volatile components evaporate and the solid mass(other 20% of initial weight) is left behind.

They are soft veges too so the material can be sweated easier than say a carrot and will lose its structure and water content at a faster rate.

Some oxidation could be occurring along with other chemical reactions between components such as decarboxylation, hydrolysis, hydration, dehydration and many more depending on what compounds are present in the process, the kind of environment (eg. aqueous) and the techniques used (eg. frying, baking).