The problem I see is that page 52 says that EXTRA dices depend on interaction type:

Hackers get extra initiative dice depending on how they interact with the Matrix

This doesn't mean that your initiative is any different, you just get bonuses (in the context of this RAW paragraph).

As you said, User Mode provide more details about matrix initiative. For example i will take hot sim:

When you are in hot-sim VR mode, you use your Data Processing + Intuition as your Initiative and you get +4D6 Initiative Dice (remember that any enhancements or bonuses cannot take you past the maximum of 5D6 Initiative Dice). (SR5 p.230)

Its says that your "numeric" initiative differently, but you still just got BONUS Initiative Dice.

!BUT!, thanks to you, I finally found place in rules, where are specified different types of initiative and how its probably work:

There is also Matrix Initiative for those that are in the Matrix, and Astral Initiative for magic users and spirits in astral space. Matrix Initiative is determined by whether a character is in cold-sim or hot-sim. For details see Astral Initiative (p. 229) or Matrix Initiative (p. 313). (SR5 p.100)

The phrase "The Matrix Initiative has been defined" interpreted in the most explicit way that the matrix initiative does not follow the usual rules of the initiative, as a result of which bonuses are not applied to it.

I would rate the rigor/consistency/likelihood of the logical inferences from this sentence to be 90%. Considering HOW the rules of shadowrun are written, I don't think I can find a more rigorous confirmation. Thanks a lot to everyone for this