How are deployment locations decided?

Here are the rules that decide what spawn locations appear in the deployment list:

• You can always spawn at your faction's warpgate.
• You can spawn at any Sunderers within 1000m.
• If your faction controls the outpost in the area where you died, you can spawn there.
• If your faction controls any neighbouring outposts, you can spawn there. (On lattice-based continents, "neighbouring" uses lattice links. On hex-based continents, this uses map hexes.)
• You always have access to the nearest major facility your faction controls. ("Nearest" is determined using either lattice links or map hexes, depending on what continent you're on.)
• Finally, the top three Instant Action locations are added to the "Reinforcements Needed" list. The algorithm that determines these spawns isn't entirely clear, but it tries to select outposts with active fights where your faction is at a slight disadvantage. (What constitutes an "active fight" and a "slight disadvantage" is frequently tweaked from patch to patch.)
• If you are in a squad, the friendly facility closest to your squad leader and any squad beacons are added to the "Squad Spawns" list.

So, to explain the screenshot you posted, where you started at the VS warpgate:

1. You can spawn at your own warpgate, because that's where you already are.
2. You can spawn at any of the three outposts connected to your warpgate.
3. You can spawn at Peris Amp Station, because it is the closest major facility.
4. Reinforcements are needed at Ti Alloys, The Crown, and Zurvan Amp Station, so you can spawn there.