Hi Srivatsan, (or can we call you Sri for short?)
I'm sure that Robert Siegel also knows that there are at least 55 different colors for the #65 stamp, with rose being one of them. They have been identified, and are well documented in The Chronicle, which is the periodical that is published by the U.S. Philatelic Classics Society.
I've been chasing these different colors now for several years (and I hope that Don is reading this and sees that I'm not calling them shades!

), and they're all identified by year and time of the year-- usually early, middle or late.
The pink stamps were the first printed, and when they found that the pink ink was not stable, they started to add some yellow in the wash and carmine. The yellow helped the stamp to become rose, and because printing and inks weren't perfect in the 1860's every batch was a little bit different.
So pink is from 1861 only. Some dated covers in 1862 can also have pink, but if it's 1863 or later, the stamp won't be certified as pink.
The darker colors, when some dark purples were added, making some of the mixtures that are Lake combinations happened in 1864. We see Lake Rose, Lake Brown, Brown Lake (yes, there is a difference), and these are all much darker even than your stamp.
If you look through my posts in the past, I've posted some examples of some of these colors of the 1861 3c #65, and some of the 64's also.
Good luck-- I love your country's stamps also, in particular the Feudatory States.....if you're ever looking to trade some for some US, please let me know!!
Thanks, and hope this is helpful! Ray
I found a few images I could share here-- Here is Lake Rose from 1863, I think a beautiful hue:

Here is a Carmine Rose from 1861:

Brownish Red Rose from 1862:

One of the Pinks...Salmon Rose Pink from 1861:

All I can post without using the Optimizer and I need to go to bed!