I haven't grown cucumbers in a container, but I'd think the same basic ideas would apply. When I first started veggie gardening I watered too much in the days following planting out. When pulled, my plants' roots looked like yours; not much there to support further health and growth. Now I use the method of: add plant, fill the planting area with water, then watch and do nothing else unless there are signs of droopy leaves in the evening -then a deep watering is applied. At that time, bottom watering of a container might be the most beneficial. Those roots need to travel downward toward the water. Once it has soaked for a time, scratch the soil surface to be sure all the soil is moist, then remove the container from the water pan.
Once you have fruit set you then will need to water more often -to fill the fruit quickly- (this helps prevent bitter fruit). But until that time you just want the plant to focus on growing great roots.
How large of a container are you using, and what's its depth? How's the drainage of the container: fast, slow or does it seem clogged?
