When message has been seen by others there is message at the end of chat message history. No text is displayed, just small avatar, but on hover there is text. On mobile this is not working so to make Seen by message more visible You need to modify:
\components\com_community\templates\jomsocial\layouts\chat\default.php
Best way to do this is to copy that file to your own JomSocial template if it does not exist already. Another way it to replicate folder structure in "code" folder in Joomla template, like:
joomla\templates\YOUR_JOOMLA_TEMAPLATE\code\components\com_community\templates\jomsocial\layouts\chat\default.php
By doing this you avoid situation where next JomSocial update would overwrite your modified files. Also, by doing this you have original files present, so if any bad thing happens you revert to original state by deleting or renaming newly created files.
What to modify:
Find <!-- Seen by template --> on line 323. Then on line 328 there is {{ } }}. New line after that and add:

<span class ="joms-chat_seen_by"><?php echo JText::sprintf('COM_COMMUNITY_CHAT_SEEN_BY', '{{= data.names }}') . '..'; ?></span>

<!-- Seen by template -->
<script type="text/template" id="joms-js-template-chat-seen-by">
    <div class="joms-chat__seen clearfix" title="<?php echo JText::sprintf('COM_COMMUNITY_CHAT_SEEN_BY', '{{= data.names }}'); ?>">
        {{ for ( var i in data.seen ) { }}
        <img src="{{= data.seen[ i ].avatar }}" />
        {{ } }}
		<span class ="joms-chat_seen_by"><?php echo JText::sprintf('COM_COMMUNITY_CHAT_SEEN_BY', '{{= data.names }}') . '..'; ?></span>
	</div>
</script>

.joms-chat__seen {
    padding: 6px 14px;
    height: 28px;
	background-color: #9bd2c2;
	margin-left: 55px;
    margin-right: 13px;
	margin-bottom: 8px
}
.joms-chat_seen_by {
	color: #12674f;
	font-size: 0.95em;
    font-weight: normal;
	line-height: 17px;
	padding-left: 8px;
}

Privet Vladimir.

Thank you for sharing this :)