Short answer: tilak is not a mandatory part of Jain abhishek. The main focus is on reverent bathing (abhishek) of the idol with water (and other offerings) and on utkars (devotion) rather than on decorative marks.

Simple guidance:

• When performing abhishek on a Jain Tirthankara idol, pour clean water or milk over the idol as a sign of purification and devotion. Then offer other approved substances (like sugar, honey, etc.) as your family tradition permits.
• Tilak on the idol: if you choose to adorn after abhishek, keep it simple and respectful. A small amount of sandalwood paste or kumkum/chandan may be lightly placed on the forehead of the idol. Do not over-decorate the idol.
• Tilak on the devotee: after finishing the puja, many people lightly apply sandalwood paste on their own forehead as a personal mark of reverence. This is optional and should be modest.

Note on Digambar vs. Shwetambar:

• Differences between Digambar and Shwetambar mainly concern scriptural emphasis and idol adornment practices. Neither tradition prescribes a universal mandatory tilak on the idol. If your local guru or temple has a specific custom, follow that with reverence.

If you want, tell me your specific tradition (Digambar or Shwetambar) and I can tailor the guidance more precisely.