The TS is facing a simple problem. She mentioned she likes her current CS jobs but gets little to no promotion / pay. And she mentioned that she has offer(/s) from private sector which let's presumes pay more.

Simple problem.
If she wants stable income in a job you like, stay.
If she wants to advance up the ranks in pay and promotion, leave for private sector.

She, and like many Singaporeans, have a attitude that their employer owes them X if they do Y. I'm very thankful for my stable progress and pay, but never once did I forget that my employer can cut me at ANYTIME.

It is the employee's responsibility to react to what market says, not the employer's. Once she does, make a choice. Follow the market which priced you better in the form of private, or accept that CS is like that. Never expect anything.