I was trying to Edit my post to get my formatting right and it seems to have locked me out so the second code snippet is slightly off because I was copying the first code section that was formatting correctly. The correct second code snippet is as follows:
<select [(ngModel)]="theme">
<option value='orange'>Orange</option>
<option value='blue'>Blue</option>
</select>
<jqxDropDownList [width]="200" [height]="height" [selectedIndex]="0" [(theme)]="theme">
</jqxDropDownList>
Where, again, theme is a string that is set on initialization as “orange” and source is an array of strings set to same dummy data. The source property was removed from this section of code and it suddenly starts picking up theme changes.