I've been playing the starbase missions like a fanatic since season 6 launch. Not once have I encountered Tholians as the enemy faction. Plenty of Klingons, Feds, Gorn, and Fek'Ihri, but no Tholians whatsoever.
My starbase is at tier 2, almost 3. Is that too low? At what tier do the Tholians start showing up?
"It's not safe out here. It's wondrous, with treasures to satiate desires both subtle and gross. But it's not for the timid."
Yeah, the starbase is chosen randomly from one of the 5 members on your team. If everyone is a member of a T3 base, then it is guaranteed to be T3. Even then though, you still only have a chance that the Tholians may show up. Otherwise you could continue to fight Klingons, Gorn, and Orion like lower tiers.
"My frozen dairy-based confectionery attracts all the males of the species to the facilities. They all agree on it's superiority. Indeed, it is superior to yours. I could teach you the finer details but that would require monetary recompense on your part." -The Milkshake Song: Vulcan Edition
I have been in a fleet alert a solid month ago with a Tier 2 starbase (i double checked) and the tholians were invading. I think earlier on, the chance of seeing tholians was slim since few were at Tier 2, and now since many fleets are, they're coming around more often.