How to say the tashahhud (Attahiyat) according the sunnah

Al-Tahiyyaatu Lillaahi wa’l-salawaatu wa’l-tayyibaat. Al-salaamu ‘alayka ayyuha’l-Nabiyyu wa rahmat-Allaahi wa barakaatuhu. Al-salaamu ‘alaynaa wa ‘ala ‘ibaad-illaah il-saaliheen. Ash-hadu an laa ilaaha ill-Allaah wa ash-hadu anna Muhammadan ‘abduhu wa rasooluh (All compliments, prayers and pure words are due to Allaah. Peace be upon you, O Prophet, and the mercy of Allaah and His blessings. Peace be upon us and upon the righteous slaves of Allaah. I bear witness that there is no god except Allaah and I bear witness that Muhammad is His slave and Messenger).
(al-Bukhaari, 831; Muslim, 402).
Then after that he should send blessings upon the Prophet (S) and say:
“Allaahumma salli ‘ala Muhammad wa ‘ala aali Muhammad kama salayta ‘ala Ibraaheem wa ‘ala aali Ibraaheem, innaka hameedun majeed. Allaahumma baarika ‘ala Muhammad wa ‘ala aali Muhammad kama baarakta ‘ala Ibraaheem wa ‘ala aali Ibraaheem, innaka hameedun majeed (O Allaah, send prayers upon Muhammad and upon the family of Muhammad, as You sent prayers upon Ibraaheem and the family of Ibraaheem, You are indeed Worthy of Praise, Full of Glory. O Allaah, bless Muhammad and the family of Muhammad as You blessed Ibraaheem and the family of Ibraaheem, You are indeed Worthy of Praise, Full of Glory).
(al-Bukhaari, 3370; Muslim, 406).

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At that point of testifying shouldn’t it be wa ashhadu ana Muhammad abduhu wa rasullu