Be aware that you might not be such a happy camper if the times fall within the hour after midnight! That code matches and captures, in the special variable $1, the two digits following a space, i.e. the hour value. It then executes (e modifier) the sprintf command in the substitution to replace the hour with a decremented value ($1 - 1). The q{ %2.2i} is the format specifier; q{ %02d} would also work. This method will break down if the hour is zero.

The simple way.

$ perl -Mstrict -Mwarnings -E '
my $dateStr = q{2016-05-16 00:51:07};
$dateStr =~ s{ (\d\d)}{ sprintf q{ %2.2i}, $1 - 1 }e;
say $dateStr;'
2016-05-16 -01:51:07
$
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A little more robust.

$ perl -MTime::Piece -MTime::Seconds -Mstrict -Mwarnings -E '
my $dateStr = q{2016-05-16 00:51:07};
my $dateFmt = q{%Y-%m-%d %H:%M:%S};
my $tp      = Time::Piece->strptime( $dateStr, $dateFmt );
$tp        -= ONE_HOUR;
say $tp->strftime( $dateFmt );'
2016-05-15 23:51:07
$
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I hope this is of interest.