Solution-focused interventions primarily focus on behavior, not on emotions
In their interventions, solution-focused professionals constantly keep on guiding clients toward behavioral descriptions of their desired situations. This helps clients to get a sense of direction, it enables them to track progress and it energizes them. In fact, as soon as positive behavior descriptions are made by clients this triggers a tendency to start performing those behaviors (more about this here). I think it is fair to say that in the solution-focused approach there is less attention to emotions. For example, neither the classic book Interviewing for solutions nor the more recent Handbook of solution-focused brief therapy even mentions the word 'emotion' in their indexes.
Solution-focused coaches generally don't ask about emotions
This is in stark contrast with other coaching and therapy approaches in which it is often common use to ask questions about emotions like: "How did you feel when that happened?", "How do you feel, right now?", "Could tell me more about your feelings?". Talking about emotions in these approaches may be based on assumptions like 1) talking about emotions may help to understand better why problems exist, 2) talking about emotions may be useful for clients as a way of letting-off steam. In the solution-focused approach these two assumptions are not held. Talking about emotions as a way of getting more information about problem causes is not useful in solution-focused coaching because, in this approach, analyzing problem causes is not part of the approach at all. Talking about emotions to help clients let off steam is also not something solution-focused coaches do because they assume that letting off steam is not required to build solutions and may even actually hurt the process of solution-building.
But the expression of emotions by clients is often a useful part of the solution-focused conversation
Having said this, it is important to stress that, in solution-focused coaching, it is certainly not a taboo to talk about problems. Solution-focused professionals trust clients to bring forward what they find most useful at any moment in the conversation, including emotions. Therefore, the expression of emotions is never discouraged. As Insoo Kim berg said, solution-focused professionals work with whatever comes back to them. It is quite common for clients to express themselves in emotional terms. Solution-focused coach will never ignore or discourage this when it happens. Instead, they will respond by appreciating their clients' concerns. When clients notice that the coach realizes that they are sad or angry and sees the merit in their concerns, this helps to strengthen the collaboration between the two and the intensity of the emotion may diminish. Then, the solution-focused coach proceeds constructively. Instead of labeling the emotions, or diagnosing their causes a follow up question is asked that will contribute to the solution-building process. As this process of solution-building proceeds positive emotions tend to emerge which have the effect of overwhelming negative emotions.