It's a small hissing sound just like if a T and an S are pronounced at the same time
I never noticed that hissing sound, but I believe I do pronounce it myself.

To produce this hissing sound (and aspiration at the same time) you should I suppose just pronounce t and d more intenensively.

There's not enough distinction between your stressed and unstressed syllables, resulting in a flat, monotonous rhythm. And in certain cases, not only the stressed syllables but entire words (including the unstressed syllables) should have a stronger intonation (for example, "...our PEOple, our TERritory, and our INterests...").
A very good recommendation.