In short, check you "column math" the program works according to my testing.

Yes I know the column here is 3rd. Let me explain the bug taking an example.

Suppose if any 2 row values of 3rd column are same (like in this case ie0hZF)

In that case it should sort by first column values of those 2 rows.

Now what if those 2 values are also same as. (like in this case - 4ewejk)

Then it will try to compare by respective 2nd column values and what if one of the value start with a digit (like in this case 4sqprx) and other with alphabet (like in this case pFnjd4) then number should come first bcoz its ascii value is less.

Which is not happening here...

If you want to compare by more than one field, this is done like this:
(extra line feeds added to prevent word wrap on the Monk page which is shorter than my standard 80 chars).

The sort{} function can even be a separate subroutine rather than the anonymous one shown here. The main point is that the "less than, equal, greater than" value is the final return statement of this anon sub and "tie breaker" is implemented as a series of logical statements. Zero (equal) is false and if that is the case, then the logical statement keeps evaluating until it runs out of "tie breaker" stuff or reaches a conclusion.

@input_lines =    
        sort {my ($a_name_last,$a_name_first,$a_city ) 
                                = split(/\s+/,$a);
              my ($b_name_last,$b_name_first,$b_city) 
                                = split(/\s+/,$b);
                   $a_name_last cmp $b_name_last
                                 or
                   $a_name_first cmp $b_name_first
                                 or
                         $a_city cmp $b_city            
                         
             }@input_lines;
[download]

Note is is possible to intermix "cmp" compares (alpha) with the "spaceship" operator <=> which is numeric only. The "standard" ways that these comparison functions work is returning (+1,0,-1) although in Perl it could be that positive value, 0, negative value works? I would stick with just +1,0,-1 if you write your own wild comparison function. I mean you can literally make a compare function where B sorts before A if you want to do that.

Update: If the context of what is being compared is known, I strongly recommend putting that application context into the code. Like above "Smith Bob Chicago" will come before "Smith Bob Houston" and is easy to see and understand.