We're having the same problem too. Our event source is JSON, and our time information looks like this:
      "start" : "2004-10-29T09:00:00-0400",
      "end" : "2004-10-29T16:00:00-0400"

Was someone able to fix this?

I will try to fix it in version 2.0. For the time being, please try to add this script after you include timeline-api.js:

<script>
Timeline.DefaultEventSource.Event.prototype.fillTime = function(elmt, labeller) {
        if (this._instant) {
            if (this.isImprecise()) {
                elmt.appendChild(elmt.ownerDocument.createTextNode(this.getProperty("start")));
                elmt.appendChild(elmt.ownerDocument.createElement("br"));
                elmt.appendChild(elmt.ownerDocument.createTextNode(this.getProperty("end")));
            } else {
                elmt.appendChild(elmt.ownerDocument.createTextNode(this.getProperty("start")));
            }
        } else {
            if (this.isImprecise()) {
                elmt.appendChild(elmt.ownerDocument.createTextNode(
                    this.getProperty("start") + " ~ " + this.getProperty("latestStart")));
                elmt.appendChild(elmt.ownerDocument.createElement("br"));
                elmt.appendChild(elmt.ownerDocument.createTextNode(
                    this.getProperty("earliestEnd") + " ~ " + this.getProperty("end")));
            } else {
                elmt.appendChild(elmt.ownerDocument.createTextNode(this.getProperty("start")));
                elmt.appendChild(elmt.ownerDocument.createElement("br"));
                elmt.appendChild(elmt.ownerDocument.createTextNode(this.getProperty("end")));
            }
        }
    };
</script>

Let me know if that helps.

Thank you for your fast response and the fix!
It helps very well!

I made the following changes to date-time.js and labellers.js; now, setIso8601Time() makes use of time zone information present in ISO timestamps instead of discarding it, labelPrecise() displays GMT offset, and parseGregorianDateTime() no longer defaults to your local time zone when dealing with timestamps without any time zone info.

<pre>
&lt;script&gt;

Timeline.DateTime.setIso8601Time = function (dateObject, string) {
    var timezone = "Z|(([-+])([0-9]{2})(:?([0-9]{2}))?)$";
    var d = string.match(new RegExp(timezone));

    var offset = 0;
    if (d) {
        if (d[0] != 'Z') {
            offset = (Number(d[3]) * 60) + Number(d[5]);
            offset *= ((d[2] == '-') ? 1 : -1);
        }
        string = string.substr(0, string.length - d[0].length);
    }

    var regexp = "^([0-9]{2})(:?([0-9]{2})(:?([0-9]{2})(\.([0-9]+))?)?)?$";
    var d = string.match(new RegExp(regexp));
    if(!d) {
        dojo.debug("invalid time string: " + string);
        return false;
    }
    var hours = d[1];
    var mins = Number((d[3]) ? d[3] : 0);
    var secs = (d[5]) ? d[5] : 0;
    var ms = d[7] ? (Number("0." + d[7]) * 1000) : 0;

    dateObject.setUTCHours(hours);
    dateObject.setUTCMinutes(mins);
    dateObject.setUTCSeconds(secs);
    dateObject.setUTCMilliseconds(ms);

    // This part was missing from dojo prior to v0.4.3, causing all sorts of trouble.
    
    if (offset !== 0) {
        dateObject.setTime(dateObject.getTime() + offset * 60000);
    }

    return dateObject;
};

Timeline.GregorianDateLabeller.prototype.labelPrecise = function(date) {
    return ((Timeline.DateTime.removeTimeZoneOffset(
        date,
        this._timeZone
    ).toUTCString()) + (this._timeZone < 0 ? "" : "+" ) + this._timeZone);
};

Timeline.DateTime.parseGregorianDateTime = function(o) {
    if (o == null) {
        return null;
    } else if (o instanceof Date) {
        return o;
    }
    
    var s = o.toString();
    if (s.length > 0 && s.length < 8) {
        var space = s.indexOf(" ");
        if (space > 0) {
            var year = parseInt(s.substr(0, space));
            var suffix = s.substr(space + 1);
            if (suffix.toLowerCase() == "bc") {
                year = 1 - year;
            }
        } else {
            var year = parseInt(s);
        }
            
        var d = new Date(0);
        d.setUTCFullYear(year);
        
        return d;
    }

    // I miss in_array() so much.
    
    var appendGMT0 = true;
    var timeZoneCodes = ["GMT", "UTC", "PST", "MST", "CST", "EST"];
    for (var i = 0; i < timeZoneCodes.length; i++) {
     if((s.match(timeZoneCodes[i])) != null) {
     appendGMT0 = false;
     break;
     }
    }
    
    if (appendGMT0 == true)
     s = s + " GMT+0000";
    
    try {
        return new Date(Date.parse(s));
    } catch (e) {
        return null;
    }
};

&lt;/script&gt;
</pre>