There's a few reasons why this could be a Moffat twist:

1. For one thing, there's her flirtatious relationship with the Doctor. She talks to him in much the same way River does - even calls him "Babes" - which is not exactly the kind of relationship he has with most people. In fact, her general attitude and many of her mannerisms seem awfully familiar. At times, it almost feels as if Tasha Lem is doing a River Song impression.
2. The Church where Tasha Lem is Mother Superious is the Papal Mainframe. This immediately suggests a possible connection to River, since we already know that when River died, the Doctor "saved" her to the mainframe of the computer in the library planet. But beyond that, we also know River has a deep connection to this very same Church. The second time we ever met her, she was working with the Church's warrior clerics to defeat the Weeping Angels. It was also the Church who kidnapped River when she was a baby and turned her into a psychopath in an attempt to keep the Doctor from ever coming to Trenzalore. It was the Church who put her in that astronaut suit and hatched the plan to murder the Doctor.
3. "You have been fighting the psychopath inside you all your life." The Doctor says those words to Tasha Lem as a reminder that she can fight the Dalek inside her, too. River Song, as mentioned above, is the other person we know who has to fight her psychopathic tendencies.
4. The Doctor also insults Tasha Lem and starts an argument with her in order to snap her out of being controlled by the Dalek inside her. "You never could resist a row," he says. That sounds a lot like River, too.
5. The Daleks say they killed Tasha Lem "several times" while they were trying to get information from her. That suggests she might be able to regenerate - an awfully rare ability. We already know River Song can regenerate thanks to being "a child of the TARDIS."
6. Tasha Lem can fly the TARDIS. "Flying the TARDIS was always easy," she tells Clara. "It was flying the Doctor I never quite mastered." There aren't many people who can fly the big blue box - but River Song was a natural at it, too.
7. The Doctor says Tasha Lem is "against aging." We already know that's one of River Song's character traits. In "The Angels Take Manhattan," she tells Amy that you need to hide the signs of your aging in order to keep the Doctor interested.
8. We already know there's something going on with River. In the season finale, she was projecting beyond the library planet mainframe, communicating with Clara. At first, it seemed like she was just using the connection with Clara that had been established during the dream "conference call." But after Clara leaped into the Doctor's timeline, River was still able to communication with the Doctor. She told him there was some unknown reason for that: a mystery still to solved. So even though she's technically dead, she may very well be able to interact with the world beyond the computer's hard drive. (Although I suppose she might have just meant the "conference call" connection was still open since Clara wasn't actually dead.)
9. River Song is also known as Melody Pond, or Mel. Lem is Mel, backwards.

1) In Flesh and Stone, The Doctor says that Amy remembers the Angels and clerics who were eaten by the crack on the Byzantium because she's a time traveler now and sees the universe differently.
2) In The Hungry Earth/Cold Blood, Amy does not remember Rory when he is absorbed by the crack deep below the Earth.

What gives?