If you did not have health insurance, yes, you need to pay the penalty for those three months.
Although your employer did not offer you health insurance, you were eligible to purchase it elsewhere, such as the Healthcare Marketplace.
However, are you sure you did not have any health insurance? As far as I understand, asylum applicants are potentially eligible for the free Medicaid health insurance (if the are unemployed). So you may want to double check to see if you were covered by Medicaid.
