Two different but related things:
Scaling in initial optimization problem provided to CVX. Try to avoid very large and very small numerical values. So improve that.
Scaling may get worse in subsequent SCA iterations. Even if scaling was good in first iteration, things can get wilder and wilder in these subsequent SCA iterations.
Starting value used in SCA might have a major impact on its evolution. Any little difference from what and how was run in the paper could cause very different outcome of SCA. You don’t know every little detail of what was done in the paper, unless they provided reproducible code for everything, including specification of computer environment, solver and tool versions and settings, etc., and of course starting values,