You can use a tag titleStyleClasstag for this <p:tab>. For instance.
<p:accordionPanel>
<p:tab title="Step 1" titleStyleClass="#{bean.step1Completed ? 'completed' : ''}">
...
</p:tab>
<p:tab title="Step 2" titleStyleClass="#{bean.step2Completed ? 'completed' : ''}">
...
</p:tab>
<p:tab title="Step 3" titleStyleClass="#{bean.step3Completed ? 'completed' : ''}">
...
</p:tab>
</p:accordionPanel>
CSS completed , true. CSS .completed {} style.css, /resources <h:outputStylesheet name="style.css">.
.completed {
background: pink;
}