You have to have at least one of the areas at Tier1 before the starbase can be upgraded.
This is probably the issue.
Look at the bars: You'll notice you're not getting Starbase XP from projects, but Military, Engineering, and Science XP.
Reach tier 1 military, and you'll unlock the military upgrade. The military upgrade will give starbase XP, which will then unlock starbase tier 1. This is why it takes 250,000 XP to reach tier 5 in each track, but only 13,000 to do so in the starbase itself.