<aura:handler name="change" value="{!v.values}" action="{!c.registerChange}" />

registerChange: function(cmp, evt, helper) {
    var cmpIsRendered = //how do I know?
    if(cmpIsRendered) {
        var value = evt.getParam("value");
        ...
    }
},

<aura:handler name="render" value="{!this}" action="{!c.componentRendered}"/>

if(!cmp.get('v.isRendered') { ... }

!cmp.set('v.isRendered') = true