The reason it is not working is because the trigger is on the sheet and not on the button. So it works with the tabs, but not when you navigate using buttons.
Solution-
Right click on the button navigating to the sheet-->Properties-->Actions
This section would already have one action (Activate Sheet)
Add two more actions-
Selection--->Clear All (After Activate Sheet)
Selection--->Select in Field (After Clear All). Here, put the field name and condition the same as behind the sheet trigger.
Apply this to all the buttons redirecting to this page. Your button navigation will now work the same as your tab navigation with default selections even in Web view.
