My ex still owes 10k in taxes from a jointly filed return in 2018. He took on the tax liability. Will my 2019 refund automatically go to paying that amount off?

It depends. If you have not filed a Form 8857, Request for Innocent Spouse Relief, for the 2018 return you may be on the hook for any outstanding balance on the return.

When you file a Married Filing Jointly return you are jointly and severally liable for the tax. Joint and several liability means that each taxpayer is legally responsible for the entire liability. Both spouses on a married filing jointly return are generally held responsible for all the tax due. This is true even if one spouse earned all the income or claimed improper deductions or credits.

I would recommend holding off on filing your 2019 tax return until you know that your ex-husband has paid the tax obligation off. You can file an extension until Oct 15th if necessary.  

You can find out more information here.