Repeat: I'm looking for a professional who understands the relativism and can answer the question: Einstein bestowed the absoluteness to the cross-scale (but not for time) - on what basis?
Masterov,
No one answers the question you have posed several times now likely for two reasons. First is we, or at least "I" am not entirely sure what you mean. And second, I am not sure Einstein ever addressed the question himself and again we, or "I" have no real idea what his thoughts were or might have been.
I can give you my thoughts on the issue, with the disclaimer that though I have read some of the older literature I have not had access to all of the literature that might have some influence on this topic and anything I say is only my opinion. (And yes I am fully aware of what some folks think about personal opinions. It really does not concern me. I remain opinionated anyway!)
In special relativity Einstein was dealing with a modernization of Relativity, which predates his efforts by several hundred years at least. His effort seems to have been largely to address Relativity from a context that incorporated Maxwell's work on electrodynamics. Hence, the title of his 1905 paper, "On the electrodynamics of moving bodies" and a flat Minkowski space-time, in which time moves in only one direction, consistent with experience.
The last three words there are perhaps significant, "consistent with experience". Einstein seemed at least in the early stages of his work to base his theoretical models on the results of experiment and experience. And time as a mater of experience moves in only one direction.
After publishing his 1905 paper on Relativity he began to explore its impact on gravity and at least two known and unresolved observations that Newton's vision of gravity could not explain, the perihelion advancement of Mercury's orbit and the apparent instantaneous action at a distance required, for Newton's field equation to be functionally accurate, which it was and remains to be.
I am not sure that anyone can truly say or know what it was that initially lead Einstein to the concept of curved space, as an explanation of the known problems of gravity at the time. It may well have been nothing more than recognizing the impact that the Lorentz Transformations would have on flat Minkowski space-time. However, he arrived at the conclusions he did, and space-time as defined from the perspective of GR became curved... And while we have experience in the world such that spacial coordinate systems can physically have meaning in all directions from a starting point, our experience of time was still limited to change progressing in only one direction, forward and into the future.
However, in associating the Lorentz Transformations with a curvature of space also came implied changes to time. Time when viewed from the perspective of a curved and dynamic space-time and the Lorentz Transformations, lost any ridged structure, and become to some extent flexible, in its rate of change. The flow of time could a can be imagined to be subject to both the curvature of space and relativistic affects, while consistent with experience it still remains constrained to motion or change in only one direction, forward and into the future.
From the perspective of GR while time cannot be imagined to change directions it can be imagined to move at differing rates depending upon the conditions within which it is viewed..., whether that is the now curved space of GR or the relativistic effects of velocity as described within SR.
Since our experience of time involves motion in only one direction, representing time as moving in two directions from a starting point or zero reference point is not consistent with experience. We can at least at present only imagine time as past, present and future and that it only moves from the present to the future, the past being as far as experience is concerned an artifact of memory. Though I am sure that the past would remain, should our memories fail, experience continues to move only into the future.