I suggest that you either invest in some self-watering planters or in a raised bed that has a solid bottom.

Roots are the tree's way of obtaining moisture and nourishment and they will just adore having lovely nutritious soil provided, along with a regular watering. That means they will make tiny rootlets to invade your garden, which also means your tomatoes are going to be bullied for root space and lose water and nutrients to the tree rootlets.

You can succeed with a raised bed providing you make the bottom root-proof by using a solid base. Metal would be best, wood or heavy plastic next. An inch of soaked newspaper over the roots *might* be enough to get you through one season. In all cases, the bed will have to have impermeable sides or else the rootlets will travel through the edges in their eagerness to get to your garden soil.

Keep in mind that both tomatoes and cukes do well in container-type growing conditions, so if you don't want to invest in planters, you can use 5-gallon buckets or small plastic garbage cans as planters. As long as you provide good soil, good drainage, sun, and regular water, the plants are not going to care whether they are in a bucket or a fancy planter. Self-watering planters are a bit of a $$ luxury but wonderful for providing steady water, which is a prime demand of tomotoes. I've used heavy plastic trash bags, and can tell you that in just a couple months the plastic gets tears and holes but otherwise does well at holding the soil. I won't use them again but they do provide a low-cost option.

Link is to one of the better self-watering garden planters. They aren't pretty (IMO) but note that they do provide a good amount of water in the base. If you are growing tomatoes, a 2 qt base for water just isn't going to make it through a really hot day.

Here is a link that might be useful: garden planters