Was my action correct when I sat for the first Tashahhud after the Imam's prostration of forgetfulness and continued the prayer, then completed the fourth rak'ah after the Imam's Taslim?

The congregant must follow the Imam in prayer. If the Imam stands up inadvertently and does not sit for the first tashahhud, the congregant must follow him and stand with him, and not remain seated. This is because if the Imam rises from the first tashahhud and the congregants remind him but he does not return, then it is obligatory for them to follow him, complete the prayer with him, and perform the prostrations of forgetfulness (sujood as-sahw) with him. Thus, those who stood with the Imam were correct, and the two individuals who remained seated were mistaken.

It has been authentically reported that the Prophet, peace and blessings be upon him, stood up from the first tashahhud, and the people stood with him and did not remain seated. When he finished his prayer, he performed two prostrations of forgetfulness before giving the salutations (tasleem), and then he gave the salutations. However, in cases of an addition to the prayer, such as the Imam standing for an extra rak'ah in the Fajr or Dhuhr prayer, they should not stand with him.