This method, like mb_ereg_search_pos, appears to use byte offsets, not character offsets. This seems counter intuitive for the mb_* methods, which inherently take a "character" view of strings, as opposed to a "byte" based view. Even the mb_strpos method returns a character offset.
The following code reveals this byte-oriented behaviour:
<?php
    $x = 'abc456789'. "\u{1000}" .'abc4567890';
    $re = 'ab.';
    echo 'x='. $x .PHP_EOL;
    echo 're='. $re .PHP_EOL;
    mb_ereg_search_init( $x );
    mb_internal_encoding( mb_detect_encoding( $x) );
    echo 'mb_strlen='. mb_strlen( $x ) .PHP_EOL;
    echo 'strlen='. strlen( $x ) .PHP_EOL;
    foreach ( array( 0, 9, 10, 11, 12, 13 ) as $o ) {
        mb_ereg_search_setpos( $o );
        echo 'Offset='. $o
            .' mb_substr='. mb_substr( $x, $o )
            .' substr='. substr( $x, $o )
            .' mb_ereg_search_regs='. print_r( mb_ereg_search_regs( $re ), true  )
            .PHP_EOL;
    }
?>
With character offsets, we would expect offsets 11 and above to return no search result, whereas what we see is:
<?php
=abc456789ကabc4567890
re=ab.
mb_strlen=20
strlen=22
Offset=0 mb_substr=abc456789ကabc4567890 substr=abc456789ကabc4567890 mb_ereg_search_regs=Array
(
    [0] => abc
)
Offset=9 mb_substr=ကabc4567890 substr=ကabc4567890 mb_ereg_search_regs=Array
(
    [0] => abc
)
Offset=10 mb_substr=abc4567890 substr=��abc4567890 mb_ereg_search_regs=Array
(
    [0] => abc
)
Offset=11 mb_substr=bc4567890 substr=�abc4567890 mb_ereg_search_regs=Array
(
    [0] => abc
)
Offset=12 mb_substr=c4567890 substr=abc4567890 mb_ereg_search_regs=Array
(
    [0] => abc
)
Offset=13 mb_substr=4567890 substr=bc4567890 mb_ereg_search_regs=
?>