When I launch the uitool-content like this :

org.ametys.uitool.ToolsManager.getInstance().openTool("uitool-content", {id: contentId, 'metadataset': metadataSet});

I show the content with main metadataSet.

We should use the asked metadataSet.
To do this, you can add the following code in org.ametys.cms.tool.content.ContentTool.prototype.refresh() method :

args += '&metadataSetName=' + this._metadataSetName;

And in org.ametys.cms.tool.content.ContentTool.prototype._updateTooltipText() method, you should have :

var params = { contentId: this._contentId, metadataSetName: this._metadataSetName };

instead of :

var params = { contentId: this._contentId, metadataSetName: 'main' };