You are correct. The employer should have added both contributions (your money and their money) and entered the total box 12 W.
You do not have to get a corrected W2, although that's an option.
When you are working of the HSA interview section, you will arrive at a question about other contributions. You will be able to add the missing amount on the line "Employer Contribution not reported on W2" (maybe not that exact wording). After completing the interview you should verify that the correct total has been reported on Form 8889, line 9 (the program automatically captures the W2 amount so don't enter that amount again).
2016