Please use the prefilled $widget_id variable.
So when you want to retrieve a field use:
get_field( 'field_name', $widget_id );
So your example would be:
<div class="exampleWidget">
<h3>This is our example widget</h3>
<p>We can grab field values like this:</p>
<?php if ( get_field( 'select_products', $widget_id ) ) : ?>
<ul class="fa-ul">
<?php while ( has_sub_field( 'select_products', $widget_id ) ) : ?>
<li>
<i class="fa-li fa fa-download"></i>
<?php the_sub_field( 'product_name' ); ?>
</li>
<?php endwhile; ?>
</ul>
<?php endif; ?>
</div>
