The code below was missing from the actual tab code that's why content didn't appeared on the first access.
Code:
$templater->register('selected_tab', $selected_tab);
So now I can have my tab as first, I can see the content when I'm accessing the profile page with &tab=dating#dating but I can't make it to be default even using Ozzy's mod.
I edit the template memberinfo:
From:
Code:
<vb:if condition="$selected_tab == 'activitystream' OR $selected_tab == ''">
To:
Code:
<vb:if condition="$selected_tab == 'activitystream'">
to avoid Activity tab to be preselected when $selected_tab == ''. I also added this condition to my own link. Nothing

Still the Activity tab is preselected (but not highlighted).
What frustates me mostly is that vB uses globally the displayorder feature. From forums to Navigation Manager. Was so big deal to add such feature for profile tabs?
--------------- Added [DATE]1413730930[/DATE] at [TIME]1413730930[/TIME] ---------------
Edited: I clear the browser's cache and now I've one more strange issue. My tab appears preselected (but not highlighted) but if you see carefully you'll find the activity report about my data. In simple words in one tab there is content of 2 tabs
http://www.xxx24.gr/member.php?3-Rene
--------------- Added [DATE]1413732196[/DATE] at [TIME]1413732196[/TIME] ---------------
Ok, Fixed after removing some code changes to member.php that I've did on the early suggestions here. Also Ozzy's mod helped me to determine the correct hook.
Instead to post the full solution here, I prefer to post an Article for those who maybe are interest to add their own tab as first tab and make it preselected. It should be a full article for building a tab. Otherwise if you've the tab ready and you just want to make it preselected,
Ozzy's mod does the work fine.
Thank you all for your help.
--------------- Added [DATE]1413735496[/DATE] at [TIME]1413735496[/TIME] ---------------
Here is the full Article for those who maybe interest for building a new tab from scratch.
https://vborg.vbsupport.ru/showthread.php?p=2519390