Short answer: In most Jain communities, no—do not use tomatoes during Paryushan.

Why:

• Many Shwetambar and Digambar households take a pachchakkhan (vow) of “harit-śāk varjan” (avoiding green/fresh vegetables) for the Paryushan/Das Lakshan days. Tomatoes are counted as śāk (vegetable), so they are avoided.
• If your personal vow is only “kand-mūl varjan” (avoiding root vegetables) and you have not taken the green-vegetable restriction, then tomatoes are generally permitted.

Follow the pachchakkhan given by your guru or local sangh. If you have taken “no green vegetables,” do not add tomatoes. If only “no roots,” tomatoes are allowed.