There are two ways that Odoo can be instructed to look for a particular view when a User navigates to a Menu:

1. Specify the View Ref for the default view (in this case the Tree/List View from the Quotations Menu):

2. Specify the Views the Action will use (in this case specific Views from the Sales Menu):

These two Actions show data from the same sale.order model differently, depending on which Menu you select.

Note: In these screenshots it appears that both Actions leverage the same View because it has the same name, but Quotations is actually using the View with External ID sale.view_quotation_tree and Sales is using the View with External ID sale.view_order_tree

I found a solution. You need to override the fields_view_get method on the model. You can match using the 'pivot_view_ref' key in the context dictionary. Here is an example:

@api.model
def fields_view_get(self, view_id=None, view_type='form', toolbar=False, submenu=False):
    view_ref = self.env.context.get('pivot_view_ref', None)
    if view_ref == '<view_name>' and view_type == 'tree':
        ref = self.env.ref('<model>.<view_name>')
        return super().fields_view_get(view_id=ref.id, view_type=view_type, toolbar=toolbar, submenu=submenu)
    else:
        return super().fields_view_get(view_id=view_id, view_type=view_type, toolbar=toolbar, submenu=submenu)