I am military and I file under a separate state than my wife. Does turbo tax system notice this and file under two separate states?

As long as you indicated the appropriate different state of residence for each spouse in the My Info section.

BUT...Folks filing different states for each spouse can get complicated, based on where you are poste, and exactly which states are involved. 

Might be better to go to a local tax service...unless you are very familiar with the complications that may be involved.

Complications:   

1)  Community property state for one, or both spouses.....must share:50/50 income on their state tax file...one or both.

2) Some states allow you to file MFJ for Federal, then require you to file MFS for the state...and that can require a separate account/tax file  (Unless using desktop software...which allows multiple files)

3)  Other states allow you to file MFJ for Federal, but then allow you to file MFJ for state, with an internal way to take out the non-resident spouse's income.

Are you filing Joint or MFS for federal?

If you need to file a Joint federal and separate state returns

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-prepare-a-joint-federal-return-and-separate-state-returns/00/25564

Reading the FAQ it looks like you have to use 3 accounts.  One to file the Joint federal return.  Then you each need another account to fill out fake federal MFS returns to do your separate state returns.    So you will have to PAY for 3 online accounts (3 federal returns and 2 state returns).  That's why it's cheaper to use the Desktop installed program.    If you don't have a computer to install the desktop program on maybe it would be cheaper and easier to go to a local accountant or tax place.

You will have to mail the 2 separate state returns.   

Online is only good for 1 return per account.  But you can use the same email address for 5 accounts.   How to start another return in the Online version

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596

Or buy the Desktop CD/Download program here

https://turbotax.intuit.com/personal-taxes/cd-download/

Be aware that Section 302 of the VBTA Act of 2018 allows the spouse of an active duty servicemember to file as a resident of the servicemember's SLR (State of Legal Residence) if they wish, even if the spouse has no other connection with that state.  This can be a very advantageous option.

https://www.congress.gov/bill/115th-congress/senate-bill/2248/text