Can any physiotherapist or psychologist issue these subsequent certificates?

No. To issue a certificate, the physiotherapist or psychologist must:

have general registration under the Health Practitioner Regulation National Law (NSW) No 86a
be providing treatment for all of a claimant’s injuries as a result of the motor accident.
refer the person back to the medical practitioner if an injured person is receiving concurrent treatment from another health practitioner
use the certificate of fitness / certificate of capacity - treating physiotherapist or psychologist form
only certify a person’s capacity for weekly entitlements