First, this is very new to me and I am only beginning to work out the implications of 'quasar variablity non-time dilation' in the SCC scenario. I may not have it right yet!
The basic premise is that it appears that observations confirm time dilation in the light profiles of distant supernovae, and, less certainly, of long GRBs, yet it is not observed in quasar variability.
One difference between these two classes is that the engines of supernovae and GRBs(?) are exploding non-degenerate (but massive) stars and the engine of a quasars is degenerate matter that has collapsed into a black hole.
Therefore there may be an explanation for this observation in SCC because in that theory the scalar field is coupled to non-degenerate matter and decoupled from degenerate matter.
How would this work?
In SCC there are two conformal frames, in the Einstein frame the cosmos evolves very much as in the mainstream model except the expansion is strictly linear with time, the universe is conformally flat the DM is all baryonic and the DE is a predetermined and measureable amount of false vacuum energy.
In the Jordan frame the universe is static and cylindrical (closed), particle masses increase exponentially with time because of the interaction of the scalar field and rulers 'shrink', cosmological red shift is a variable mass effect.
There are two processes involved in observing quasar variability, which may be understood in the Jordan frame.
The first is the red shift observed in emission lines from the accretion disk. The atoms in the past were less massive and therefore emitted at a lower frequency than at present, which is observed as a cosmological red shift.
Secondly the time scale of the variability is dependent on the size of the accretion disk itself. This diameter is determined by the gravitational field which itself is dependent on the mass of the central black hole.
Whereas the masses of individual atoms increase over cosmological time the mass of the black hole does not, because it does not interact with the scalar field. Its mass increases only through accretion, it does not increase cosmologically.
Therefore the time scale of the variability of the quasars emission should not be red-shift dependent.
The question of whether the light curve of a super nova should show time dilation in a variable mass cosmology was discussed by Narlikar & Arp in the paper: TIME DILATION IN THE SUPERNOVA LIGHT CURVE AND THE VARIABLE MASS HYPOTHESIS
I would appreciate comment and constructive criticism!