Super Agents generally (outside of specific story events) just visit your base if you are Starting a Scheme in a region of the world they are currently watching. If you Start and Complete a Scheme there they will get a team of Agents together and visit your lair.
The only successful Scheme that doesn’t Trigger a Super Agent visit in a region currently being watched is a long-term Heat Reduction one (30 minutes) using 3 Workers/Valets/Spin Doctors or similar. Upgrading your Criminal Network also doesn’t do it. Any Scheme that will end up in the region getting locked down will abort upon Lockdown and also not draw a Super Agent, similarly with say a long-term money Scheme that is aborted at 95%.
If you have Faction coverage of several Scouted regions (like for instance North-Eastern and North-Western for P.A.T.R.I.O.T.) the Super Agents are more likely to appear in an area you don’t usually have important Events and Quests in like Greenland or Canada, and leave you alone to do your missions in the areas that actually matter like the East Coast of the US. If you only have 2 regions they just alternate between the two and are even more annoying to deal with on the World Map.
Once you’ve gained their attention on the World Map because you have started and finished a Scheme in a region they were watching, you have 1-3 Minutes to intervene and send minions to reduce the amount or Skill of Agents that will arrive with the Super Agent. The Super Agent will always come, but they’ll have weaker Squads.
When they visit your base, as long as they aren’t Combat types like Atomic Olga, who comes with a squad of armed Soldiers, they will do their intended job and leave your base without attacking. Symmetry for instance will appear with her team within your vault, steal all your gold, then run around your base a lot and leave by Speedboat. Agent X will appear in the Middle of your base with an Investigative team and try and gather evidence (or plant it), then leave the island. They usually won’t attack you till you tag them for Killing/Capture.
If it comes to a fight, Workers are almost completely useless against higher Level Super Agents and their teams. Your Evil Genius and Henchmen are your primary Super Agent combat units early in the game. Make sure to walk them close to the action and trigger their combat Skills when necessary. Waiting to engage into combat with them while outside an Armory with 1-2 fully staffed Guard tables with Muscle Minions like Guards or Mercenaries (best if armed) might also be a good idea. Don’t start a fight in the Mess Hall if you’re not ready to deal with a lot of Worker bodies.
Symmetry (A.N.V.I.L. Super Rogue) – Spawns in your Vault with a Squad of Rogues, steals your gold and tries to get away via Speedboat if not prevented. Gold and any items that her team might have stolen drop on the ground if they’re killed/interrogated/brainwashed
Agent X (P.A.T.R.I.O.T. Super Investigator) – Spawns in the Middle of your base with a Squad of Investigators and will try to gather (or plant) evidence and get away
John Steele (Super Saboteur) – Comes alone from the Helicopter platform via Speedboat and will try to blow up parts of your Lair by planting dynamite
Atomic Olga (H.A.M.M.E.R. Super Soldier) – Usually comes from the Helicopter platform via Speedboat with a Squad of Soldiers and will attack immediately after entering the base
Wrecking Bola (S.A.B.R.E. Super Saboteur) – Comes from the Helicopter platform via Speedboat with a Squad of Saboteurs and will try to blow up parts of your Lair by planting dynamite
Blue Saint (S.M.A.S.H. Super Saboteur) – Comes from the Helicopter platform via Speedboat with a Squad of Saboteurs and will try to blow up parts of your Lair by planting dynamite