  We propose a model of the evolution of the tachyonic scalar field over two
phases in the universe. The field components do not interact in phase I, while
in the subsequent phase II, they change flavours due to relative suppression of
the radiation contribution. In phase II, we allow them to interact mutually
with time-independent perturbation in their equations of state, as Shifted
Cosmological Parameter (SCP) and Shifted Dust Matter (SDM). We determine the
solutions of their scaling with the cosmic redshift in both phases. We further
suggest the normalized Hubble function diagnostic, which, together with the
low- and high-redshift $H(z)$ data and the concordance values of the present
density parameters from the CMBR, BAO statistics etc., constrains the strength
of interaction, by imposing the viable conditions to break degeneracy in
3-parameter $(\gamma, \varepsilon, \dot{\phi}^2)$ space. The range of redshifts
$(z=0.1$ to $z=1.75)$ is chosen to highlight the role of interaction during
structure formation, and it may lead to a future analysis of power spectrum in
this model \emph{vis a vis} Warm Dark Matter (WDM) or $\Lambda$CDM models. We
further calculate the influence of interaction in determining the age of the
universe at the present epoch, within the degeneracy space of model parameters.
