Some portion of slab is used by many engineers to take into the account the effect of line load on the slab. Many call it a beam, because the reinforcement arrangement resembles like a beam. But it cannot technically be called a beam; beam is a member that attracts force by virtue of its stiffness. Since, the thickness of so called beam is equal to that a slab, it cannot attract forces.
It is a simplified way of taking into the account the effect of line load on slab; by arranging reinforcement in this way, one assumes that the effect of line load will be limited within the width of so called beam. So the width of the beam will be decided by the design moment.
The beam will be only designed for the load of the supported wall, or the load of supported wall + the load transferred by the wall from upper levels. The so called beam cannot take any load from adjacent slab area, as it does not have the stiffness to attract any load. So tributary area thing is not applicable to that member.
If you understand what is written above, you should conclude that there is no need to check the deflection.
In many cases, this way of locally reinforcing the slab ( so called concealed beam) will not be able to support the load transferred from above levels, unless you increase the thickness of slab.