I got this to work on a per column basis:

http://jsfiddle.net/GDW13/y3DHn/1/

Code:
Ext.tip.QuickTipManager.init();

Ext.create('Ext.data.Store', {
    storeId:'employeeStore',
    fields:['firstname', 'lastname', 'seniority', 'dep', 'hired'],
    data:[
        {firstname:"Michael", lastname:"Scott", seniority:7, dep:"Management", hired:"01/10/2004"},
        {firstname:"Dwight", lastname:"Schrute", seniority:2, dep:"Sales", hired:"04/01/2004"},
        {firstname:"Jim", lastname:"Halpert", seniority:3, dep:"Sales", hired:"02/22/2006"},
        {firstname:"Kevin", lastname:"Malone", seniority:4, dep:"Accounting", hired:"06/10/2007"},
        {firstname:"Angela", lastname:"Martin", seniority:5, dep:"Accounting", hired:"10/21/2008"}
    ]
});

cellTooltipRenderer = function(value, metaData, record, rowIdx, colIdx, store) {
    var column = this.headerCt.getGridColumns()[colIdx];
    var newVal;
    switch (column.xtype) {
    case 'booleancolumn':
        newVal = Ext.create('Ext.grid.column.Boolean').defaultRenderer(value);
        break;
    case 'datecolumn':
        newVal = Ext.create('Ext.grid.column.Date', {format: column.format}).defaultRenderer(value);
        break;
    case 'numbercolumn':
        newVal = Ext.create('Ext.grid.column.Number').defaultRenderer(value, column.format);
        break;
    case 'templatecolumn':
        newVal = Ext.create('Ext.grid.column.Template', {tpl: column.tpl}).defaultRenderer(value, metaData, record);
        break;
    case 'actioncolumn':
    default:
        newVal = value;
    }                        
    metaData.tdAttr = 'data-qtip="' + newVal + '"';
    return newVal;
};
        
Ext.create('Ext.grid.Panel', {
    title: 'Column Demo',
    store: Ext.data.StoreManager.lookup('employeeStore'),
    columns: [
        {text: 'First Name',  dataIndex:'firstname', renderer: cellTooltipRenderer},
        {text: 'Last Name',  dataIndex:'lastname', renderer: cellTooltipRenderer},
        {text: 'Hired Month',  dataIndex:'hired', xtype:'datecolumn', format:'M', renderer: cellTooltipRenderer},
        {text: 'Department (Yrs)', xtype:'templatecolumn', tpl:'{dep} ({seniority})', renderer: cellTooltipRenderer}
    ],
    width: 400,
    forceFit: true,
    renderTo: Ext.getBody()
});
It's not intended to be used with Action columns but it works with the other column types.