No. Tirthankaras are not born only to Jain parents.

• They are born as ordinary children in worldly families, often in royal or noble lineages, and in various regions of ancient India.
• Their family’s religious affiliation is not required to be Jain. After growing up, they renounce the worldly life and attain enlightenment, becoming teachers who establish the Jain path.
• There are differences in details across Digambar and Shwetambar canonical accounts about the exact family backgrounds of each Tirthankar, but the consistent point is that they come from non-Jain households who later realize and teach the Jain Dharma.