The only problem with spading under fallen and leftover tomatoes is the likelihood that seeds will survive the winter and produce volunteer plants the next year. The fruits are unlikely to be a disease vector. Trying to compost the fruits is unlikely to kill the seeds as many will survive temperatures higher than anyone is likely to get in an autumn compost pile. Unless you can have a separate compost pile or bin for tomatoes and their relatives, turning under chopped vines is better than putting remains in your compost.
Rotating the crop is essential for disease control in organic growing with tomatoes, potatoes, peppers, eggplant and okra collectively being in the same ground no more frequently than one year in four. Otherwise diseases are likely to build up and require fungicides.