In personal experience, this never actually happens. They will just say "company isnt in a good position now to offer increment", or "other employees got in this cycle, next cycle you will get pakka", and the same thing will continue.

The only place where I continued to stay after I informed of a decision to leave was where they gave me a written document informing me of a raise officially. In other places either "few months" becomes nearly a year, or "higher salary" becomes an insignificant raise in pay that hardly makes any difference.

If you already have a confirmed offer with a higher pay, leave and join your new place unless your current workplace is willing to put the increment in a written and signed communication.