That lawyer has definitely no idea about TPS.
Unless some lawyer contradict me with solid proof, my understanding which is true is...
TPS is designed for those whose visas are expiring soon but not able to go to own country because of the situation of the country.
If your visitor visa/status/I-94 duration of status is valid till USCIS receives your TPS application and your visa/status expires before TPS approval, your stay in US during TPS processing will not be considered an unlawful.
If your visitor visa/status has expired before USCIS receives your TPS application and you overstayed, only the days from visa expiry to USCIS reciept date will be considered as unlawful presence.
Definitely if TPS is denied, then your presence will be considered unlawful from the day your visa/status expired.
Even for people entering US illegally, if their TPS is approved, their presence in US is considered legal from the day USCIS receives the TPS application