Your code seems ok to me:

c:\@Work\Perl\monks>perl -wMstrict -le
"my @strings = (
   'SMS,SMS1,20190811',
   'SMS,SMSh,20190811',
   'SMS,SMSH,20190811',
   'SMS,SMSx,20190811',
   'SMS,SMSi,20190811',
   'SMS,SMSX,20190811',
   'SMS,SMSI,20190811',
   );
 ;;
 for my $s (@strings) {
   my $ref_s = \$s;
   print qq{'$$ref_s' matches}
     if $$ref_s =~ /SMSi/i
     || $$ref_s =~ /SMSI/i
     || $$ref_s =~ /SMSh/i
     || $$ref_s =~ /SMSH/i
     || $$ref_s =~ /SMS1/
     ;
   }
"
'SMS,SMS1,20190811' matches
'SMS,SMSh,20190811' matches
'SMS,SMSH,20190811' matches
'SMS,SMSi,20190811' matches
'SMS,SMSI,20190811' matches
[download]

What am I doing differently from what you're doing?

Update 1: Here's a variation showing assignment via reference (and aliasing). Again, I think it works the way I think you think it should work. (Maybe take a look at Short, Self-Contained, Correct Example.)

c:\@Work\Perl\monks>perl -wMstrict -MData::Dump -le
"my @strings = (
   'SMS,SMS1,20190811',
   'SMS,SMSh,20190811',
   'SMS,SMSH,20190811',
   'SMS,SMSx,20190811',
   'SMS,SMSi,20190811',
   'SMS,SMSX,20190811',
   'SMS,SMSI,20190811',
   );
 ;;
 for my $s (@strings) {
   my $ref_s = \$s;
   $$ref_s = 'SMSblk'
     if $$ref_s =~ /SMSi/i
     || $$ref_s =~ /SMSI/i
     || $$ref_s =~ /SMSh/i
     || $$ref_s =~ /SMSH/i
     || $$ref_s =~ /SMS1/
     ;
   }
 ;;
 dd \@strings;
"
[
  "SMSblk",
  "SMSblk",
  "SMSblk",
  "SMS,SMSx,20190811",
  "SMSblk",
  "SMS,SMSX,20190811",
  "SMSblk",
]
[download]

Update 2: BTW: I'd tend to write something like this a bit differently:

c:\@Work\Perl\monks>perl -wMstrict -MData::Dump -le
"my @strings = (
   'SMS,SMS1,20190811',
   'SMS,SMSh,20190811',
   'SMS,SMSH,20190811',
   'SMS,SMSx,20190811',
   'SMS,SMSi,20190811',
   'SMS,SMSX,20190811',
   'SMS,SMSI,20190811',
   );
 ;;
 for my $s (@strings) {
   my $ref_s = \$s;
   $$ref_s .= ' is SMSblk' if $$ref_s =~ /SMS[iIhH1]/;
   }
 ;;
 dd \@strings;
"
[
  "SMS,SMS1,20190811 is SMSblk",
  "SMS,SMSh,20190811 is SMSblk",
  "SMS,SMSH,20190811 is SMSblk",
  "SMS,SMSx,20190811",
  "SMS,SMSi,20190811 is SMSblk",
  "SMS,SMSX,20190811",
  "SMS,SMSI,20190811 is SMSblk",
]
[download]

And maybe also throw in some kind of boundary assertion like  \b so the final regex might look like
    / \b SMS[iIhH1] \b /x
to prevent a string like  'SMS,xSMSHx,20190811' from matching.