h:commandLink renders data table but p:commandLink does not

Question

I'm trying to migrate an application from RichFaces to PrimeFaces 10.0. As part of it, there is a search link which when clicked performs the actions method returns a list of cars populated by a p:dataTable. The data table is rendered if the command link is h:commandLink but is not rendered if replaced with p:commandLink. Is there any additional tag that needs to be added to the p:commandLink for the table to be rendered?

<h:form id="example">
<h:panelGrid columns="3" id="searchId">
    <h:commandLink id = "cmdd" value="Search" action="#{carBean.searchCars}"/>
</h:panelGrid>

<h:panelGrid id="panelGroup" style="width:100%" styleClass="tblNowrap100pct">
    <p:dataTable value="#{carBean.carList}" var="car" id="carTbl" 
                 stripedRows="true" rendered="#{not empty carBean.carList}"
                 showGridlines="true" styleClass="tblNowrap100pct"
                 filteredValue="#{carBean.filteredValues}" rowKey="#{car.carId}"> 

    <p:column headerText="Car Name" sortBy="#{car.carName}" filterBy="#{car.carName}" filterMatchMode="contains" >
            <f:facet name="header">
                    <h:outputText value="Car Name" />
            </f:facet>
                    <h:outputText value="#{car.carName}" />
    </p:column>

  <p:column  headerText="Make"    sortBy="#{car.make}"  filterBy="#{car.make}" filterMatchMode="contains">
            <f:facet name="header">
                    <h:outputText value="Make" />
            </f:facet>
                    <h:outputText value="#{car.make}" />
   </p:column>
</p:datatable>
</h:form>

The above code does not render the data table when replaced with p:commandLink. When replacing with p:commandLink the action method is invoked and the list is populated but is not getting rendered in the xhtml page.

public void searchCars() {
   try {
       this.carList = carService.searchAllCars(this.carDto);
       if (carList.isEmpty()){
           FacesMessage message = new FacesMessage("No records found.");
           FacesContext context = FacesContext.getCurrentInstance();
           context.addMessage(null, message);
       }
    }
    catch(Throwable exception){
        ...
    }        
}

*Edited to added a couple of columns to the datatable which is not rendered if the commandlink is a primefaces command link