I bought The Witness, it auto installed on my iPhone (which is so annoying) and I uninstalled it but now it's asking me to rebut it to install it on the iPhone. However on my iPad it's still working and says I own it... huh?
I've seen that happen. If you input your password to purchase it, it should tell you that you already own it and can download it again for free. It should also show up under your purchases. Obviously, I make no guarantees but I've never been charged twice for something since 2008.
Funny, I bought the same app earlier tonight. It installed on my phone, but never finished on my iPad. Finally I went to start over and it disappeared. Then it wanted me to repurchase it. I went to the Today tab, click on the silhouette in the upper room gut and went to Purchased. Then I was able to redownload it. It must be a bug.