This is exactly how 'Surya Namaskar' should be done!
‘Surya Namaskar' or Sun salutation is above any other form of Yoga. It not relieves the mind but also activates the body ‘chakras'.
‘Surya Namaskar' is the best form of Yoga and should be done every morning to get eternal bliss. It is in no way restricted to any particular religion. It can be done by any one as Sun is same for all, irrespective of his or her religion.
The only important thing is that it should be done in a correct manner.
Though it takes time to learn it, but once learnt it is no less than bliss for a person as the 12 ‘asanas' of ‘Surya Namskar' trigger the 7 ‘chakras' of our body.
So, learn it the correct way. Even if you are already doing it, still watch the video to know if you are doing it in the correctly or not.