A workaround is to force the tooltip to update its position when the content arrives (i.e., in the OnClientResponseEnd event: http://www.telerik.com/help/aspnet-ajax/tooltipmanager-client-side-on-response-end.html )
function OnClientResponseEnd(sender, args) {
var activeTooltip = Telerik.Web.UI.RadToolTip.getCurrent();
if (activeTooltip) {
activeTooltip.updateLocation();
}
}
Not reproducible - FF 37 and Telerik.Web.UI.dll version 2015.1.401