While this is at least an attempt to justify your assertion. The above all rests on the assertion that all observers in question (Albert Henry and Evelyn) assume coordinate systems are physical. This is the exact opposite of how reference frames are employed.
"In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
Evelyn's reference frame, like Henry's and Albert's, is a mathematical construct, describing what a hypothetical observer would observe. Hence, nobody concludes two clocks are intrinsically ticking faster than each other, or themselves. They instead construct what observers would measure, and relate these measurements via Lorentz transformations.
Again, the conlcusion is that a clock is measured to tick both faster and slower than itself.