"However, in this case, the $name is in the second column (1), and the last column is 9. The first column is where "MCCCC... " is located."

I suspect there's something here you haven't understood but I don't know what that might be.

The " MCCC processed: ..." and "station, ..." lines have already been read in the for loop; they're not read again in the while loop. The first line read in the while loop will be:

 ZJ.GRAW    -0.7964    0.0051    0.9690    0.0139    0  GRAW.BHZ   301
+.1263    -1.8041
[download]

When split on whitespace, element zero will be "ZJ.GRAW".

In your next split, element zero is the only element where you're likely to capture "ZJ". Your split pattern is wrong here but I'll assume that's progated from earlier errors (obviously, you want to split on /[.]/ — not /\s+/).

Beyond all these issues, splitting on whitespace, and then trying to recreate the line, without knowing how much whitespace originally existed will not work: you won't retain the "same formatting" you state you want. So, I suggest you sit back and think of another approach.

Assuming you've provided representative data, here's how I might have tackled the logic. (Note: I'm assuming "remove the mean" indicates subtracting the mean: if not, modify the calculation in output_recalc_zj_lines() to suit.)

#!/usr/bin/env perl

use strict;
use warnings;

print scalar <DATA> for 1 .. 2;

my @zj_lines;

while (<DATA>) {
    if (/ \A Mean_arrival_time: \s+ ( \S+ )/x) {
        output_recalc_zj_lines(\@zj_lines, $1);
        print;
        last;
    }
    
    push @zj_lines, $_;
}

print <DATA>;

sub output_recalc_zj_lines {
    my ($zj_lines, $mean) = @_;

    for (@$zj_lines) {
        s/ ( \S+ ) ( \s+ ) \z / $1 - $mean . $2 /ex;
        print;
    }
}

__DATA__
 MCCC processed: unknown event at: Tue, 14 Oct 2014 12:02:26 CST 
station, mccc delay,    std,    cc coeff,  cc std,   pol   , t0_times 
+ , delay_times
 ZJ.GRAW    -0.7964    0.0051    0.9690    0.0139    0  GRAW.BHZ   301
+.1263    -1.8041
 ZJ.KNYN     -0.7065    0.0072    0.9760    0.0133    0  KNYN.BHZ   30
+1.3372    -1.9249
 ZJ.LEON      0.9675    0.0072    0.9548    0.0292    0  LEON.BHZ   30
+1.2611    -0.1749
 ZJ.RKST     -0.2061    0.0114    0.9404    0.0383    0  RKST.BHZ   30
+1.3500    -1.4374
 ZJ.SHRD      0.4382    0.0051    0.9542    0.0351    0  SHRD.BHZ   30
+1.7360    -1.1791
 ZJ.SPLN      0.3033    0.0051    0.9785    0.0126    0  SPLN.BHZ   30
+1.0760    -0.6541
Mean_arrival_time:   300.1187 
No weighting of equations. 
Window:   2.23   Inset:   1.17  Shift:   0.25 
Variance: 0.00645   Coefficient: 0.96215  Sample rate:   40.000 
Taper:   0.28 
Phase: P        
PDE    2013  7 15 14  6 58.00   -60.867   -25.143   31.0  0.0  7.3
[download]

Output:

$ pm_1126698_split_record.pl
 MCCC processed: unknown event at: Tue, 14 Oct 2014 12:02:26 CST 
station, mccc delay,    std,    cc coeff,  cc std,   pol   , t0_times 
+ , delay_times
 ZJ.GRAW    -0.7964    0.0051    0.9690    0.0139    0  GRAW.BHZ   301
+.1263    -301.9228
 ZJ.KNYN     -0.7065    0.0072    0.9760    0.0133    0  KNYN.BHZ   30
+1.3372    -302.0436
 ZJ.LEON      0.9675    0.0072    0.9548    0.0292    0  LEON.BHZ   30
+1.2611    -300.2936
 ZJ.RKST     -0.2061    0.0114    0.9404    0.0383    0  RKST.BHZ   30
+1.3500    -301.5561
 ZJ.SHRD      0.4382    0.0051    0.9542    0.0351    0  SHRD.BHZ   30
+1.7360    -301.2978
 ZJ.SPLN      0.3033    0.0051    0.9785    0.0126    0  SPLN.BHZ   30
+1.0760    -300.7728
Mean_arrival_time:   300.1187 
No weighting of equations. 
Window:   2.23   Inset:   1.17  Shift:   0.25 
Variance: 0.00645   Coefficient: 0.96215  Sample rate:   40.000 
Taper:   0.28 
Phase: P        
PDE    2013  7 15 14  6 58.00   -60.867   -25.143   31.0  0.0  7.3
[download]

Note how the original formatting is retained exactly (including the space that is presumably missing between ZJ.GRAW and -0.7964 which, if present, would have aligned that record's format with the other ZJ records).