If you activate task or calendar synchronization, yasoon always adds a category "basecamp". In the settings you may have choosen to add other categories as well, e.g. the project name.
These categories are white per default. If you want to assign a color to one of these categories, simply open a task/appointment with that category, click on the standard Outlook category button and choose “all categories”. Here you can see the basecamp categories. Select one and click on new to choose a color of your choice.
You only need to do that once for each category. All other tasks with that category get the same color as well.