The plugin just makes the "normal" date available even if you have "detailed" selected. To see any change you need to edit your postbit or postbit_template and insert {vb:raw post.postdate_normal} where you want the normal date to appear.
So if you're using postbit_legacy (post info on the left side) then you could edit that template and find this section:
Code:
<vb:else />
<span class="date">{vb:raw post.postdate}<vb:if condition="!$show['detailedtime']">, <span class="time">{vb:raw post.posttime}</span></vb:if></span>
</vb:if>
and maybe change it to this:
Code:
<vb:else />
<span class="date">{vb:raw post.postdate}<vb:if condition="!$show['detailedtime']">, <span class="time">{vb:raw post.posttime}</span><vb:else /><vb:if condition="isset($post[postdate_normal])"><vb:if condition="$post[postdate_normal] !== $post[postdate]"> {vb:raw post.postdate_normal}</vb:if>, <span class="time">{vb:raw post.posttime}</span></vb:if></vb:if></span>
</vb:if>