mIRC 7.33
Quote:
53.Added CAP server-time and znc.in/server-time[-iso] support. Enabled
automatically with a CAP request if server lists it in CAP LS. If a
server message has a @time prefix with a UTC timestamp, $msgstamp
will return this value.


In mIRC 7.33 and newer, you will no longer see those *** Buffer playback / *** Playback complete lines.

http://ircv3.atheme.org/extensions/server-time-3.2

I use something like this for my znc 1.6.0/mIRC 7.41, I guess this is what you are after?
Code:
on ^*:TEXT:*:#: {
  if ($nick == *buffextras) {
    var %nick = $gettok($1,1,$asc(!))

    ; Timestamp format -- CHANGE ME for different formats. /help $asctime
    var %format [HH:nn:ss]

    if ($3 == MODE:)       echo $color(mode) $chan $asctime($msgstamp,%format) * %nick sets mode: $4-
    elseif ($2 == JOINED)  echo $color(join) $chan $asctime($msgstamp,%format) * %nick ( $+ $gettok($1, 2, $asc(!)) $+ ) has joined $chan
    elseif ($2 == QUIT)    echo $color(quit) $chan $asctime($msgstamp,%format) * %nick ( $+ $gettok($1, 2, $asc(!)) $+ ) Quit ( $+ $4- $+ )
    elseif ($2 == PARTED)  echo $color(part) $chan $asctime($msgstamp,%format) * %nick ( $+ $gettok($1, 2, $asc(!)) $+ ) has left $chan
    elseif (($2 == IS) && ($3 == NOW)) echo $color(nick) $chan $asctime($msgstamp,%format) * %nick is now known as $6
    elseif ($2 == KICKED)  echo $color(kick) $chan $asctime($msgstamp,%format) * $3 was kicked by $gettok($1,1,$asc(!)) ( $+ $4- $+ )
    elseif ($2 == CHANGED) echo $color(join) $chan $asctime($msgstamp,%format) * %nick changes topic to ' $+ $6- $+ 03'
    else                   echo $color(erro) $chan *** UNHANDLED LINE < $+ $1- $+ >
    halt
  }
}

I guess you want "var %format [mm/dd/yy HH:nn:ss]" in that example above to match your first picture?