JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jstree/3.1.0/jstree.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/jstree/3.1.0/themes/default/style.min.css">
<div id="jstree"></div>

CSS

.jstree-contextmenubtn { position:relative; cursor:pointer; }

JavaScript

// additional icon on node (outside of anchor)
(function ($, undefined) {
	"use strict";
	var img = document.createElement('IMG');
	img.src = "http://jstree.com/tree-icon.png";
	img.className = "jstree-contextmenubtn";

	$.jstree.plugins.contextmenubtn = function (options, parent) {
		this.bind = function () {
			parent.bind.call(this);
			this.element
				.on("click.jstree", ".jstree-contextmenubtn", $.proxy(function (e) {
						e.stopImmediatePropagation();
                        $(e.target).closest('.jstree-node').children('.jstree-anchor').trigger('contextmenu');
					}, this));
		};
		this.teardown = function () {
			this.element.find(".jstree-contextmenubtn").remove();
			parent.teardown.call(this);
		};
		this.redraw_node = function(obj, deep, callback, force_draw) {
			obj = parent.redraw_node.call(this, obj, deep, callback, force_draw);
			if(obj) {
				var tmp = img.cloneNode(true);
				obj.insertBefore(tmp, obj.childNodes[2]);
			}
			return obj;
		};
	};
})(jQuery);

$('#jstree').jstree({
    core : {
        check_callback : true,
        data : [
            { "id" : "1", "parent" : "#", "text" : "root" },
            { "id" : "2", "parent" : "1", "text" : "child 1" },
            { "id" : "3", "parent" : "1", "text" : "child 2" }
        ],
    },
    plugins : ["wholerow","contextmenu","contextmenubtn"]
}).on("ready.jstree", function (e, data) {
  data.instance.open_all();
});