In Titan TakeOver, progression works through Titan Tiers.
When your Faction knocks out a Titan, the next Tier unlocks.
Each new Tier is harder but gives better rewards.
The unlocks are tied to your Faction.
Once a Tier is unlocked, it stays open for that Titan as long as your Faction holds it.
If you switch to another Faction, their Tier progress may be different.