After you file

Yes, it's very normal. The accepted in TurboTax will remain that way from here on out. That just lets you know the government received your return. There are no further updates to be provided to TurboTax. From this point forward, you'll check your status of your returns with the IRS and/or your state. 

Processing times can vary depending on how large of a backlog the government is working on. Once they are done processing the return, they will approve your refund and provide a deposit date (or check mailed date).

You can use the IRS Where's My Refund site for the latest status on your federal tax refund.

And you can use your State Department of Revenue's website to check status of state tax refund. Choose your state here How do I track my state refund? and it will give you steps to track the status.  

If you claimed Earned Income/Additional Child Tax credit on your return, the government held those returns until mid-February. And refunds from those returns will start releasing in late February. You can find more details on that here Avoid the Rush Track Tax Refund Online at IRS.gov