For a discrete time unit step signal \$u(n)\$ , if time reversal operation is performed then it becomes \$u(-n-1)\$. Is it true for any discrete time signal \$x(n)\$ such that time reversal operation makes it \$x(-n-1)\$?
Yes, you can picture it by looking at the time index (n in your case) as going from -infinity on the left to infinity on the right.
What does time reversal mean? Your function values (e.g., step function values) will reverse, as time "moves" from right to left instead (for example, instead of having the value 0 from -infinity to -1 and then having 1 from 0 to infinity, it would become 0 from infinity to 0 and then 1 from -1 to -infinity). So, yes, from reasoning about it, you can see that it is true for any discrete time signal.