From acoustical point of vew, it could be different distance causing different retarded times of the signals:
$$
t_{set \ one} = \tau_{of \ the \ speaker} - \frac{r_{to \ set \ one}}{c_0}
$$
$$
t_{set \ two} = \tau_{of \ the \ speaker} - \frac{r_{to \ set \ two}}{c_0}
$$
But if one of the set is let's say cable TV and the other e.g. internet TV, there might be small lags between the signal, i.e.:
$$
\tau_{of \ the \ speaker \ 1} \neq \tau_{of \ the \ speaker \ 2}
$$
The other effect might be reflections in long hallways causing more difference in $r$s from the first formula.
Mentioned diametrical opposition would lead to interference, but thet would not be percieved as reverberation, but as changes of sound volume. Anyway, with complex and generally short and complex sounds (speech, jingles, gunfire...) it would not be significant.