interval.php

<?php

$messages = [
    [
        'start'    => '11:00', // Datetime
        'end'      => '14:00', // Datetime
        'interval' => '10',    // display every x minutes
        'text'     => 'top',   // The text to display
        'duration' => 2       // duration of the display in minute
    ],
    [
        'start'    => '10:00',
        'end'      => '12:00',
        'interval' => '30',
        'text'     => 'toto',
        'duration' => 10
    ],
];

function getMessageWithTime($message) {
    $result = [];
    $current = $message['start'];

    while ($current < $message['end']) {
        $result[] = array_merge($message, ['start_time' => $current, 'end_time' => $current + $message['duration']]);
        $current = $current + $message['interval'];
    }

    return $result;
}

function getMessagesWithTime($messages) {
    $result = [];
    foreach ($messages as $message) {
        $result = $result + getMessageWithTime($message);
    }

    return $result;
}


$result = getMessagesWithTime($messages);


$result = [
    [
        'start'      => '10:00',
        'end'        => '12:00',
        'interval'   => '30',
        'text'       => 'toto',
        'duration'   => 10,
        'start_time' => '10:00', //You have your start time
        'end_time'   => '10:01'  //You have your end time
    ],
    [
        'start'      => '10:00',
        'end'        => '12:00',
        'interval'   => '30',
        'text'       => 'toto',
        'duration'   => 10,
        'start_time' => '10:30',
        'end_time'   => '10:31'
    ],
    [
        'start'      => '10:00',
        'end'        => '12:00',
        'interval'   => '30',
        'text'       => 'toto',
        'duration'   => 10,
        'start_time' => '11:00',
        'end_time'   => '11:01'
    ],
    [
        'start'      => '10:00',
        'end'        => '12:00',
        'interval'   => '30',
        'text'       => 'toto',
        'duration'   => 10,
        'start_time' => '11:30',
        'end_time'   => '11:31'
    ],
    ...
];