A sample project for reproducing the issue is attached:

Each of the pages in the ContentUrl properties has an alert("PageName") displayed at pageLoad.

1, Brows the Default.aspx - an alert - page1 occurs

2. Select Level 2 tab, which would load the subTab - Page4 and the "page4" alert should be shown.

Problem : In addition to the "page4" alert - the "page5" alert is raised and the page5.aspx had been loaded along with page4.aspx.

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Workaround:
To workaround this issue, set the PageViewID property of the parent tab to be with the same value as the PageViewID property on the selected child tab.

<telerik:RadTabStrip runat="server" ID="RadTabStrip1" MultiPageID="rmpPages" Width="100%">
    <Tabs>
        <telerik:RadTab Text="Level 1" Selected="true" PageViewID="page1">
            <Tabs>
                <telerik:RadTab Text="Page 1" PageViewID="page1" Selected="true" />
                <telerik:RadTab Text="Page 2" PageViewID="page2" />
                <telerik:RadTab Text="Page 3" PageViewID="page3" />
            </Tabs>
        </telerik:RadTab>
        <telerik:RadTab Text="Level 2" PageViewID="page4">
            <Tabs>
                <telerik:RadTab Text="Page 4" PageViewID="page4" Selected="true" />
                <telerik:RadTab Text="Page 5" PageViewID="page5" />
                <telerik:RadTab Text="Page 6" PageViewID="page6" />
            </Tabs>
        </telerik:RadTab>
    </Tabs>
</telerik:RadTabStrip>

<telerik:RadMultiPage runat="server" ID="rmpPages">

    <telerik:RadPageView runat="server" ID="page1" ContentUrl="page1.aspx" Selected="true" />
    <telerik:RadPageView runat="server" ID="page2" ContentUrl="page2.aspx" />
    <telerik:RadPageView runat="server" ID="page3" ContentUrl="page3.aspx" />
    <telerik:RadPageView runat="server" ID="page4" ContentUrl="page4.aspx" />
    <telerik:RadPageView runat="server" ID="page5" ContentUrl="page5.aspx" />
    <telerik:RadPageView runat="server" ID="page6" ContentUrl="page6.aspx" />

</telerik:RadMultiPage>