They both have to be protected, but only for half as long, as the knowledge is accumulated at twice the rate. The game does try to avoid this, but on some maps it's unavoidable.
If the game is actively trying to avoid placing both Spire Archives on the same planet, there is a bug. Take a look at this screenshot - Two archives on the same planet, when there were 10 possible worlds they could have gone on (5 for one homeworld, 5 for the other).
It may not happen every time, but often enough. This was the second map I created to check. Of 10 maps I checked, 5 were good, 2 were bad (both Archives in the same system) and 3 were mixed (both archives near only one homeworld).