It depends on the type of trigger you use.  Publications support 3 types of triggers: Schedule Trigger, Report Trigger and Page Trigger.

Schedule triggers determine whether or not a schedule is actually run. These triggers DO NOT look at the slicer values.  

Report triggers determine whether or not a specific report should be generated.  You can create these triggers by clicking on the Report Trigger Manager button on the main Publication toolbar. You can pass the slicer value to the trigger via the trigger dialog box (see example below).

 Page triggers determine whether or not a specific page in the report should be generated.  You can create these triggers by clicking on the Page Trigger Manager button on the Page toolbar. You can pass the slicer value to the trigger via the trigger dialog box (see example below).  You want to make sure you apply the trigger to the correct page using the Page drop-down.