In the game we played, both of the players were able to acheive space victory in the same turn - who won? Is it a tie, or is there a tiebreaker that we didn't see in the rules?

From the FAQs on the support page:

"Q. If multiple players finish a tech victory on the same turn, who wins?"

"A. The player who is first in the turn order wins. Alternately, players may choose to play with the Advanced Tie-Breaker Variant listed in this
document."

Check the FAQs on the support page, they also have an alternative for tie-breaking simultaneous victories.

Admje14 said:

What the privious person said. here's the Variant

Advanced Tie-Breaker Variant
If a player completes a military victory, the game ends immediately and that player wins. If a player completes a culture, economic, or technology victory, the rest of the turn is played out. After the end of the turn, every player who has completed a non-military victory (remembering that military victories instantly win the game) calculates their victory score, as follows:
Victory Score = Number of Learned Technologies + Number of Spaces Advanced on Culture Track + Number of Coins
The player with the the highest Victory Score wins the game. In the event that two or more players are still tied, then they share the victory.