Can you explain me why I received a Illinois paper asking me more payment ?

No one can explain that to you, since no one at TurboTax can see your tax return or the letter you received from IL.  Read your letter more carefully to see what it says, and provide more details.  TurboTax does not receive any information about your return after you file it.

and..

You are posting from TurboTax Live. If you used "Live" to prepare your 2018 return, and the letter is about your 2018 IL return, you can arrange for the Live help you are paying the extra fee for with your questions from  5 a.m. to 5 p.m. Pacific time Monday - Friday.

https://ttlc.intuit.com/questions/4124827-how-do-i-connect-with-a-tax-expert-in-turbotax-live