<div data-jmpress="drive-right after 1s step">This will drive in.</div>
</div>
Then I tried this (do not ask why):
<div id="regions" class="step slide" data-jmpress="drive-right after step">
  <div data-jmpress="drive-right after 1s step">This will drive in.</div>
</div>
and make it work! Animation became operate without pressing the buttons. Then I removed the data-jmpress = "drive-right after step" from the parent DIV and everything will work all the same. Strange.
New problem :) The hint displaying stopped when idle. I don't know why does not work standard code:
Jmpress page's code:
...
<div id="jmpress">
     <div id="FIRSTSCREEN" class="step slide" data-x="-1000" data-y="-1500" data-z="0">
          <div class="child"  data-jmpress="drive-right after 2s step"><q><b>Республика Казахстан</b></q>
          </div>
     </div>
...
</div>
<div class="hint">
    <p>Для просмотра используйте клавишу "пробел" или кнопки со стрелками <br />Use a spacebar or arrow keys to navigate</p>
</div>
    document.querySelector(".hint").innerHTML = "<p>Tap on the left or right to navigate</p>";
}
</script>
<script src="js/jmpress.all.js"></script>
<script>$(function() {
    $('#jmpress').jmpress();
});</script>
CSS code:
...
.hint {
    display: none;
    position: fixed;
    left: 0;
    right: 0;
    bottom: 200px;
    background: rgba(0,0,0,0.5);
    color: #EEE;
    text-align: center;
    font-size: 40px;
    padding: 20px;
    z-index: 100;
    opacity: 0;
    -webkit-transform: translateY(400px);
    -moz-transform:    translateY(400px);
    -ms-transform:     translateY(400px);
    -o-transform:      translateY(400px);
    transform:         translateY(400px);
    -webkit-transition: opacity 1s, -webkit-transform 0.5s 1s;
    -moz-transition:    opacity 1s,    -moz-transform 0.5s 1s;
    -ms-transition:     opacity 1s,     -ms-transform 0.5s 1s;
    -o-transition:      opacity 1s,      -o-transform 0.5s 1s;
    transition:         opacity 1s,         transform 0.5s 1s;
}
.jmpress-enabled .hint { display: block }
.jmpress-on-FIRSTSCREEN .hint {
    opacity: 1;
    -webkit-transform: translateY(0px);
    -moz-transform:    translateY(0px);
    -ms-transform:     translateY(0px);
    -o-transform:      translateY(0px);
    transform:         translateY(0px);
    -webkit-transition: opacity 1s 5s, -webkit-transform 0.5s 4.5s;
    -moz-transition:    opacity 1s 5s,    -moz-transform 0.5s 4.5s;
    -ms-transition:     opacity 1s 5s,     -ms-transform 0.5s 4.5s;
    -o-transition:      opacity 1s 5s,      -o-transform 0.5s 4.5s;
    transition:         opacity 1s 5s,         transform 0.5s 4.5s;
}
...
Where is my mistake? Earlier the hint was displayed at the right time (as in impress.js, and after the transition to jmpress.js, too). I can not remember a time when a hint ceased to be displayed.
Thanks!