If I have a Hwei and one hidden Tideturner at a battlefield, and my Hwei gets pulled to the other battlefield by Blitz, can I react by playing Tideturner? Or is the battlefield no longer under my control?

Yes, you can react by playing Tideturner from hidden.

According to Rule 187.4.c and the corresponding clarifications, control of a battlefield cannot be lost while there are items on the chain.

When your opponent plays Blitzcrank and triggers his "When you play me" ability, that triggered ability is placed on the chain. Because there is an item on the chain, you do not lose control of your battlefield when Hwei is moved to the other battlefield, even if Hwei was your only unit there.

Here is the sequence:

1. Blitzcrank enters play: His "When you play me" triggered ability is placed on the chain, targeting your Hwei.
2. Chain State: The state is now CLOSED (there is an item on the chain).
3. Reaction Window: Because the chain is not empty, you have a window to play reactions. Playing a card from "Hidden" is a reaction (Rule 811.1.b, Rule 737.6).
4. Action: You can reveal and play your hidden Tideturner. Even though your battlefield would normally trigger a cleanup to remove hidden cards after losing your only unit, that cleanup is suppressed because an item (the Blitzcrank ability) is still on the chain.

You may play Tideturner in response to the Blitzcrank ability to swap him with a unit at another location, or simply to place him onto the board before the Blitzcrank ability resolves. Note that Tideturner's ability to swap units also uses the chain, and targeting is determined upon resolution.