I trued my wheel yesterday a bit, since many spokes lost some tension. Once I finished, all spokes were quite rigid.
Then I put the new tire on and as I was inflating it, I heard the spokes loosen up, with a typical cling, as heard while truing. The tension adjustment seems to have gone.
The tire was indeed hard to put on, but after inflation it fits the rim properly, no part of the tire is sunk inside. The pressure is also correct, 0.4 MPa (the max pressure allowed being 0.45 MPa).
In theory, the inner tube expands equally strong in all directions, so also inwards; however I have not observed visible contraction of the rim so far, even in the cheap $15 models.
Maybe a wheel should be trued with the tire on?