Allowed ROTH IRA contribution causes tax bill???

The Roth IRA contribution interview will tell the the reason - what does it say?

Only enter the contribution after all other income has been entered.  The contribution might be limited or denied if not enough taxable compensations or too high a MAGI.

The most you can contribute to all of your traditional and Roth IRAs is the smaller of:

For 2018, $5,500, or $6,500 if you’re age 50 or older by the end of the year; or
your taxable compensation for the year.
For 2019, $6,000, or $7,000 if you’re age 50 or older by the end of the year; or
your taxable compensation for the year.

(Taxable compensation is generally wages that you worked for - W-2 or net self-employed income minus the deducible part of the SE tax, but can include commissions, certain alimony and separate maintenance, and nontaxable combat pay ).

See IRS Pub 590A "What is compensation" for details:
https://www.irs.gov/publications/p590a#en_US_2018_publink1000230355

See this IRS article for Roth contribution limits:

https://www.irs.gov/retirement-plans/roth-iras

A $360 penalty corresponds to an excess contribution of $6,000, not $5,500.

The penalty will be present until you have entered your W-2(s) with box 1 amounts (reduced by any amount in box 11) totaling at least the amount of your Roth IRA contribution.  The contribution will also be an excess contribution if your modified AGI for the purpose exceeds the limit corresponding to your filing status.  To see if the excess contribution penalty is actually still present, check Schedule 2 line 6 after making all of the entries.

Also be aware the any earnings excluded under the Foreign Earned Income Exclusion (if any) are not earnings that will support an IRA contribution.