now should i tell my employer that i forgot my update my td1 last year when i had two jobs and they need to redo my tax calculations all over again for 2017 or will they fire me for the trouble? and which td1 form should i have updated i the first place, the first employer, the second's or both?
The TD1 is just the personal credits form. You should complete it yearly to ensure you're having enough tax deducted at the source. The best way to ensure you'll owe less tax next year is to fill out the TD1 for the 2nd employer and indicate that you have another job. On page 2 of the form, there's a section for "More than one employer or payer at the same time". That's the section that's most important for you.
There's no need to worry. Your employer won't have to do anything extra - no need to recalculate anything from 2017. Going forward, your payroll deductions will just be updated once you submit the form. The TD1 isn't mandatory except when you begin a job but it's a good idea to complete it yearly to avoid owing a big tax bill!