Approach 1

You have some unclosed Tags. After i changed the code as follows and it worked for me.

tabs.xhtml

<h:form  prependId="false" id="form">
    <p:tabView id="tabPanel" widgetVar="tabPanel" binding="#{myBean.tabView}" dynamic="true" activeIndex="0">

        <!-- FIRST TAB -->
        <p:tab id="person" title="Person">
            <h:panelGrid columns="2" cellpadding="10">              
                <h:outputText value="name" />
                <p:inputText value="???USERINFO???" label="Name" />
                <p:commandButton  value="NEXT" action="#{myBean.nextButton}" update=":form:tabPanel" immediate="true"/>
           </h:panelGrid>
        </p:tab>


        <!-- SECOND TAB -->
        <p:tab id="adres" title="Address">
            <h:panelGrid columns="2" cellpadding="10">
                <h:outputText value="Phone" />
                <p:inputMask id="phone" value="???USERINFO???" mask="1999999999" required="true" requiredMessage="ERROR AT PHONE NUMBER"/>
                <p:commandButton  value="NEXT" action="#{myBean.nextButton2}" update=":form:tabPanel" immediate="true"/>
            </h:panelGrid>
        </p:tab>

        <!-- THIRD TAB -->
        <p:tab title="Contact">
            <h:panelGrid columns="2" cellpadding="10">
                <h:outputText value="CONTACT" />
            </h:panelGrid>
        </p:tab>    
    </p:tabView>
</h:form>

MyBean.java

@ManagedBean(name = "myBean") 
@RequestScoped
public class MyBean implements Serializable {

    private static final long serialVersionUID = 2431097566797234783L;

    private TabView tabView;

    public TabView getTabView() {
        return tabView;
    }

    public void setTabView(TabView tabView) {
      this.tabView = tabView;
    }

    public void nextButton()
    {
        tabView.setActiveIndex(1);
    }

    public void nextButton2()
    {
        tabView.setActiveIndex(2);
    }
}

Approach 2

For me switching from ViewScopedto RequestScopeddid the trick. If i were you, i would do the following:

Remove the binding from the tabView.

<p:tabView id="tabPanel" widgetVar="tabPanel" dynamic="true">

Switch tabs with JavaScript.

<p:button onclick="PF('tabPanel').select(1);return false;" value="NEXT" />

...instead of...

<p:commandButton  value="NEXT" action="#{myBean.nextButton}" update=":form:tabPanel" immediate="true"/>

Approach 3

This third approach works with ViewScoped bean and without binding.

Remove the binding and map the activeIndex of the TabView to a property.

<p:tabView id="tabPanel" dynamic="true" activeIndex="#{myBean.activeIndex}">

On the next button, call an action which increments the activeIndex property.

<p:commandButton  value="NEXT" action="#{myBean.nextTab}" update=":form:tabPanel" />

tabs.xhtml

<h:form id="form">
    <p:tabView id="tabPanel" dynamic="true" activeIndex="#{myBean.activeIndex}">

        <!-- FIRST TAB -->
        <p:tab id="person" title="Person">
            <h:panelGrid columns="2" cellpadding="10">              
                <h:outputText value="name" />
                <p:inputText value="???USERINFO???" label="Name" />
                <p:commandButton  value="NEXT" action="#{myBean.nextTab}" update=":form:tabPanel" />
            </h:panelGrid>
        </p:tab>                     

        <!-- SECOND TAB -->
        <p:tab id="adres" title="Address">
            <h:panelGrid columns="2" cellpadding="10">
                <h:outputText value="Phone" />
                <p:inputMask id="phone" value="???USERINFO???" mask="1999999999" required="true" requiredMessage="ERROR AT PHONE NUMBER"/>
                <p:commandButton  value="NEXT" action="#{myBean.nextTab}" update=":form:tabPanel" />
            </h:panelGrid>
        </p:tab>

        <!-- THIRD TAB -->
        <p:tab id="contact" title="Contact">
            <h:panelGrid columns="2" cellpadding="10">

            </h:panelGrid>
        </p:tab>             

    </p:tabView>
</h:form>   

MyBean.java

@ManagedBean(name = "myBean") 
@ViewScoped
public class MyBean implements Serializable {

    private int activeIndex = 0;

    public int getActiveIndex() {
        return activeIndex;
    }

    public void setActiveIndex(int activeIndex) {
        this.activeIndex = activeIndex;
    }

    public void nextTab() {
        activeIndex++;
    }
}