  A quantum tricritical point is shown to exists in coupled time-reversal
symmetry (TRS) broken Majorana chains. The tricriticality separates
topologically ordered, symmetry protected topological (SPT), and trivial phases
of the system. Here we demonstrate that the breaking of the TRS manifests
itself in an emergence of a new dimensionless scale, $g = \alpha(\xi) B
\sqrt{N}$, where $N$ is the system size, $B$ is a generic TRS breaking field,
and $\alpha(\xi)$, with $\alpha(0)\equiv 1$, is a model-dependent function of
the localization length, $\xi$, of boundary Majorana zero modes at the
tricriticality. This scale determines the scaling of the finite size
corrections around the tricriticality, which are shown to be {\it universal},
and independent of the nature of the breaking of the TRS. We show that the
single variable scaling function, $f(w)$, $w\propto m N$, where $m$ is the
excitation gap, that defines finite-size corrections to the ground state energy
of the system around topological phase transition at $B=0$, becomes
double-scaling, $f=f(w,g)$, at finite $B$. We realize TRS breaking through
three different methods with completely different lattice details and find the
same universal behavior of $f(w,g)$. In the critical regime, $m=0$, the
function $f(0,g)$ is nonmonotonic, and reproduces the Ising conformal field
theory scaling only in limits $g=0$ and $g\rightarrow \infty$. The obtained
result sets a scale of $N \gg 1/(\alpha B)^2$ for the system to reach the
thermodynamic limit in the presence of the TRS breaking. We derive the
effective low-energy theory describing the tricriticality and analytically find
the asymptotic behavior of the finite-size scaling function. Our results show
that the boundary entropy around the tricriticality is also a universal
function of $g$ at $m=0$.
