How do I know that the tax was filed through TurboTax?

There could be a couple or reasons why you might be experiencing a delay;

1. First, the status might be pending for security reasons. This may be a sign that someone is trying to use your identity to file a tax return. The return has been placed on hold to give you an opportunity to cancel it if it doesn't belong to you. This can take up to 72 hours, after which your return will then be forwarded to the IRS, or if applicable, rejected. If rejected, you can then correct the rejection issue and resubmit. Please see this FAQ for reference.

2. Secondly, there could be a delay if your return has various refundable credits, such as the Earned Income Credit.

Note: Both instances may be applicable. That is, you could have a hold for security reasons first. And additionally for verification of the refundable credits in your return. In this case, delays might extend beyond 72 hours.

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.

Once your return is filed, TurboTax has no control over the processing of your return or the release of your refund.

Here are a couple FAQs to track your refund:
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?