Unlockable contacts
Global rule. If you have the badge at the appropriate level, the contact will open up. If you get the badge after the fact, you can do the content through Ouroboros.
Paragon Wiki: http://www.paragonwiki.com
City Info Terminal: http://cit.cohtitan.com
Mids Hero Designer: http://www.cohplanner.com
So if I get the Bling badge at level 23, say, and hit level 25, Doc Buzzsaw should pop-up as a contact?
She didn't. That's what lead me to believe its maybe per-badge.
I'm not sure the contact would just "pop up" on it's own. The contact is unlocked, but you were not introduced to him. If you manually go and talk to him once you reach the correct lvl, he should then appear on your list and give you missions.
I have never had Doc not be awarded to a villain who got the Bling badge, before or after 25. Did you attempt to talk to her? That should be the obvious next step.
Paragon Wiki: http://www.paragonwiki.com
City Info Terminal: http://cit.cohtitan.com
Mids Hero Designer: http://www.cohplanner.com
I never tried to talk to her in person, I just checked my contacts list to see if she was there.
That explains that, then. Thanks for clearing this up.
During Double XP Weekend, I had a character earn the Bling badge before 25. As soon as I trained them up to 25, Doc Buzzsaw pop'd up as a new contact.

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The unlockable contacts in the Rogue Isles typically require you to be in a level range and to get a specific badge.
If you get the badge after you've outlevelled the level range, you miss out.
But what happens if you get the badge before the level range?
For example, I got "Bling" on one character in the late teens/early 20's and Doc Buzzsaw never popped up as a contact, suggesting that you need to gain the badge whilst in the level range 25-29 in order to get her.
Paragon Wiki on the Slot Machine contact says:
"If you reach the levels shown with the badge and have not visited the Slot Machine already, it will introduce itself to you from level 30 onwards. " suggesting that getting the badge first and then hitting the level range does unlock this contact.
Does this vary between contacts, or is there a global rule?