Q:

Is it common to pronounce two /tjuː/?

The word "two" in a tutorial sounds like /tjuː/ at multiple positions.
Is it common to pronounce two /tjuː/?
Another tutorial uses the same pronunciation.

I want you to listen to English through this lens that I'm giving you, right?

A:

Yes, I see what you mean. I think what you're hearing is the aspiration of the "t". For example, in "two stews" [tʰu: stu:z] the first "t" is aspirated and the second isn't. In your first linked example, it seems to me that the sound was recorded by the microphone in a way that emphasized sibilant and aspiration type sounds, more than you might hear by listening to someone in person. If you were to pronounce "two" unaspirated as [tu:] instead of [tʰu:], it would likely sound too much like "do".
When I say that it is aspiration, I mean that it is interpreted by myself and I assume most native English speakers to be this. It's possible that I hear a palatalized [tʲ] as an allophone of the aspirated "t". Note that you can't use an affricated "ch" [t͡ʃ] here in my dialect, as <ch> is a separate sound in English.

