Phantom Province Houserule
There is certainty a first-player advantage in Dominion. However, that particular house rule gives a possibly even more significant second-player advantage. The reason for this is that the first player can never safely end the game. He has very little control over how the game ends. The best he can do is to build up a significant lead, then end the game and hope. Meanwhile, the second player (assuming a 2 player game) can end the game exactly when he needs to in order to win.

There is a lot of discussion about this exact rule here: http://forum.dominionstrategy.com/index.php?topic=9791.0.

And here is a well-written article explaining the reasons behind the first-player advantage:
http://forum.dominionstrategy.com/index.php?topic=1467.0

There are definitely statistics to support this advantage. http://councilroom.com/ contains statistics from thousands of online Dominion games with top players. You can pick almost any good player at random and see that their win percentage as first player is much higher than their win percentage as second player. It appears that the search functionality on councilroom is down at the moment, but here is a link to statistics gathered from there: http://forum.dominionstrategy.com/index.php?topic=54.msg723#msg723. Finally, there is a lot of discussion on the statistics of first-player advantage here: http://forum.dominionstrategy.com/index.php?topic=946.0.

This advantage was designed to be countered by playing multiple games, and having the winner go last in the next game, which is actually written in the original instruction book.