How close to water do my tomatoes need to be to considered irrigated?

I don't irrigate them at all, the people in the village water them, if it is marked as field. Irrigitation would probably remove the need to water them.

The water block needs to touch the planted block in order to be naturally irrigated. Water also occasionally falls from the sky ;)

Also, also, if you have a way to carry water, you can literally pour it on your crops, then just scoop it up again if you don't like the water sitting around everywhere.