Thank you for the report! Logged in GitBug:
It also doesn't work in IE10 and Safari. I didn't test others. Here is a test case.
<%@ Page Language="C#" %>
<title>Ext.NET v3 Example</title>
<ext:ResourceManager runat="server" />
<ext:TextField runat="server" Text="Some text" SelectOnFocus="true" />
Found this Sencha bug report which is marked as fixed in ExtjS 5.1.2. So, the fix will come to Ext.NET with the next ExtJS upgrade.
Before the fix comes I can recommend this solution:
<ext:TextField runat="server" Text="Some text">
<Focus Handler="this.inputEl.dom.select();" Delay="1" />