Can you still get a transcendence victory if the enemy built a mind flower first?

The victory page seems to indicate that I just wait... is the enemy on a different timer?

Exactly that. The initial time span can be shortened by building the Xeno Sanctuary and the Mind Stem in your cities.

Assuming two players finish the Mind Flower the same turn, the player with more cities having a Xeno Sanctuary and a Mind Stem will essentially win (due to faster point generation).

You can delay a Transcendence Victory by destroying those buildings/raiding the cities with them.

If you'd like to cut-off some other player's progress, you'll have to attack and destroy the Mind Flower.

Just keep in mind that this victory condition might be slightly bugged according to Reddit.