Turbo tax used wrong time zone

No, your return will still be considered filed on time, even though you waited until the last moment to file it. 

When you say 'should i pay the IRS directly even though I already paid TurboTax?' do you mean that you paid your tax due through your return?

If that's the case, don't pay the IRS again.

I paid my tax due via turbo tax. However, it’s been 1.5 hours and I still haven’t received an email saying my return was transmitted, the main page in turbo tax says pending and $0 taxes. The e-file details section still says not received by California. 

If the page says pending, then wait. The state usually follows the federal return. 

Same thing happened to me, just now.  It's 11:15PM in my time zone on April 15, but TurboTax is saying the return was filed at 12:15AM on April 16.

I did take a screenshot - though I suspect I'm still screwed....

You can check that your return was received by the taxing authority  using these instructions: Check the Electronic Postmark of your Return. Pay close attention to the separate lines for Federal and State. They are separate statuses.

Thank you. Turbo tax did not transmit my state tax return until today, April 16 at 3:42 am pacific. I e-filed at 9:02pm. What do I do now that they submitted it late?

You are ok, as long as you submitted it by the deadline. The time they acknowledged can be after the deadline.

Turbo tax now says they received my tax return on April 16 at 3:42am and transmitted it the same time. Yesterday the file detail showed turbo tax received it at 9:02pm April 15. Why did turbo tax do that? I have a screen shot. Do I need to contact anyone? Thanks! 

Interesting. I wouldn't worry about it at this point. Especially with the state.