I have seen some muslims don't pray after salaat, they used to say, praying to Allah after salaat is not a part of salaat. Then why do some of them are praying after salaat?

There are many different opinions of scholars. Mostly having to do with being sunni or shia (and others)

Some do not believe that Dua is required after Salah.

Most Muslims I have met and learned from, it IS a requirement.

So I am unsure what the true answer is.

My suggestion would be to continue what YOU believe. And continue to follow your Imams instructions.

Assalamu Alaikum