I was praying a two rakat prayer today, but after reciting my tashahud in my sitting position, instead of moving onto the durood and then salam, I accidentally stood up for a third rakah.
I only realized my mistake when I was halfway through the Fatiha. Upon realizing my mistake I immediately sat back down and performed sajdah sahw by reciting the tashahud again, making salam only to the right, and then making the two sajdahs. After coming up from the second sajdah, I finished normally by reciting tashahud, durood, dua and then salam.

Did I perform sajdah sahw correct? And must one always reciting tashahud first before performing the sajdah sahw?