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If you are not-claiming the tax-free threshold you will have tax taken out of every dollar, so there is likely to be an error.
It's likely that the payroll administrator of the second job has wrongly selected that you were claiming the tax-free threshold.
Payroll errors are some of the most common I've seen personally. It's not difficult for them to make an adjustment and catch-up any additional tax you may need to pay, but it will mean you get less take-home pay over a period of time while you catch-up, have the discussion with them.
If you're concerned about your current tax return and you end up with an amount payable, you can also talk to the ATO to arrange a payment plan if paying the full amount is too difficult.
Best bet is to expect the worst, which may be a payable amount on your 2019 tax return and knowing that it isn't the end of the world, because the ATO does understand individual challenges and can be fairly accomodating.