Whether you are transplanting tomatoes to a larger container or they are going into the garden, a little care can make a lot of difference.
1. Swirled roots.
Tomatoes have massive root systems and can quickly fill a container. Even if they are not fully root bound, if you find your plants are swirling their roots around the inside of the container gently move them away. By loosening them up they will be more likely to spread out when transplanted. If they are left to their own devices, they may continue to swirl even though they have plenty of room.
2. Multiple plants.
The traditional method to deal with more than one plant per pot is to pinch or cut one off, usually the smaller of the two. But many gardeners, myself included, hate to see any plant go to waste.
I have found it better to let the plants grow until the final container. Even though the root systems are more entwined than at seedling stage, they have so much more roots that they seem to recover from the division faster.
I will admit I usually limit my plants to 2 per cup. Dividing 3 can be tough if they are very close together.
3. Keep them out of the light.
Transplanting is stressful to the plant. Either leave your plant light off for the rest of the day, or when transplanting outside choose a cloudy day. In a pinch you can cover your plants with the cup they were in. Just give them a chance to settle in before they are back in the light.