So they didn't clarify regarding your notice period as stated as 2 month, like whether you can shorten etc.? What was your response?

If they didn't ask, keep it at that I suppose. Anyway, you gave short notice to your current coy ah?

I'm thinking that in the event they were to find out and ask, perhaps you can say that you managed to shorten your notice period only after confirming your start date with the new coy or you already have a plan trip and didn't want to take leave during probation period or when you just started work that kinda thing.