In order to show custom message on linked WebCombo scenario, you can try to use following approach.

1. Set ParentEmptyAction property to “ShowEmptyResult”
   By default, the value of this property is PromptMessage where the combo will prompt a message if the ParentWebCombo contains no value. If the value of this property is set to ShowEmptyResult, the combo will show empty result when the ParentWebCombo contains no value.

<ISWebCombo:WebCombo ID="wcManager" runat="server" ...>
    <LinkSettings Enabled="True" ParentWebComboID="wcDivision" ParentEmptyAction="ShowEmptyResult" />
</ISWebCombo:WebCombo>

2. Add a WebDialogBox to the page that will be shown when ParentWebCombo contains no value
   Add a WebDialogBox and write down the custom error message.

   <ISWebDesktop:WebDialogBox ID="WebDialogBox1" runat="server" DialogBoxImage="Information"
       Height="150px" Width="400px">
       <ContentTemplate>
           Please enter the Division name to continue.
       </ContentTemplate>
   </ISWebDesktop:WebDialogBox>

3. Add OnShowDropDown client-side event handler on the ChildWebCombo (wcManager)
   The OnShowDropDown client-side event specifies the client-side (JavaScript) function that will be invoked when the ResultBox is about to show.

   <ISWebCombo:WebCombo ID="wcManager" runat="server" ...>
       <LayoutSettings>
           <ClientSideEvents OnShowDropDown="wcManager_OnShowDropDown" />
       </LayoutSettings>
       <LinkSettings Enabled="True" ParentWebComboID="wcDivision" ParentEmptyAction="ShowEmptyResult" />
   </ISWebCombo:WebCombo>

4. Show WebDialogBox if ParentWebCombo contains no value
   In wcManager OnShowDropDown check whether the wcDivision has value or not. If the wcDivision has no value, show WebDialogBox by invoking ShowDialog() method.

   function wcManager_OnShowDropDown(controlId, left, top, width, height) {
       var wcDivision = ISGetObject("wcDivision");
       var wcManager = ISGetObject(controlId);
       var WebDialogBox1 = ISGetObject("WebDialogBox1");
   
       if (wcDivision.Value == "") {
           WebDialogBox1.ShowDialog();
           return false;
       }
   
       return true;
   }

I enclosed one simple sample of your scenario as attachment. Please have the attached sample tested on your end and let us know whether it suits to your scenario or not.

Hello Jean,

If you would like to change the message, you can simply change in TextSettings properties  (child WebCombo).

e.g 

 <TextSettings ParentEmptyPromptText="{0} value should be selected" />

However, you could not change the style of its style because it is browser alert.
I suggest you to use WebDialogBox as the workaround. In this case, you will need to use "ShowEmptyResult" value in LinkSettings>>ParentEmptyAction properties.

This value would ignore the alert or any messages. Then, show WebDialogBox in OnShowDropDown clientside events. By using WebDialogBox as the message, you can configure freely your message style.
For further information, please see Yudi's reply. He posted a simple sample about how to use WebDialogBox for your scenario.

Regards,
Handy

Hello,

Yudi's proposed solution works beautifully.

Thanks.

Jean