Question

Can the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow?

Answer 1

"We see that the original perturbation with nonzero conformal spin generates the perturbation with zero conformal spin".

There in fact it considers the effect interchain of hopping term between two spinless fermionic chain . The original perturbation means the interchain hopping term in bosonization language as (or see the formula (8.9) at page 64 in the book I mentioned above):
V=g∫dzdz¯cos(βΦ)cos(β¯Θ)
V=g∫dzdz¯cos⁡(βΦ)cos⁡(β¯Θ)
And the perturbation generated by this term under the RG procedure are (see page 66, (8.18))
V1V2=g1cos(2βΦ)=g2cos(2β¯Θ)(β<β¯)(β>β¯)

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Answer 2

yes the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow.