How to explore with wormhole generator in Eclipse?
You are correct that you must select the unexplored space you wish to explore before drawing the hex tile from the appropriate stack. And yes, if you have the wormhole generator technology, you may explore a space adjacent to a side of your controlled hex that does not have a wormhole half. However, you must then make sure you orient the new hex so that a half wormhole is positioned next to that side of the new hex. If you look at the examples on page 9 of the rulebook the hex marked D, which is a legal placement for a player with a wormhole generator, is an example of the above described situation.