Have you ever tasted a tomato leaf? If I were a bug, would stick with the beans, peppers and cucumbers too. The problem with Neem is that it takes awhile to work - up to two weeks. If you use it when you first plant and before you see bugs, Neem has a much better chance at controlling insects. I would avoid Sevin also. My go to is commercially made Insecticidal Soap. It works by turning insect shells into jelly (and then they die).
Unless you are getting the plants wet in the hot afternoon sun, watering and fertilizing are done when its convenient for you. But you should have a schedule as plants do better that way. Inconsistent watering will lead to blossom end rot on your tomatoes.