SYMPTOM:
A searchbox selector does not filter down the attribute elements when it is targeted by another selector, in Strategy Web 9.3.0.
STEPS TO REPRODUCE:

CAUSE:
This is a current limitation of Strategy Web 9.x. The searchbox selector cannot read the XML file created by any other type of selector in order to interact with it and filter its results further down. Therefore, the elements returned by the searchbox selector are not filtered. However an enhancement request has been logged to address this behavior.
ACTION:
This issue is fixed in Strategy 10.x and above for Presentation Mode. Upgrade and use Presentation Mode to take advantage of this fix.
WORKAROUND:
Use any other type of selector except for the searchbox selector.