As far as I know, data tips only turn on if you turn them on (either programmatically or using the builtin MATLAB figure toolbar). So you should be able to just avoid doing that.
In a separate but related recent question, I found this code snippet that appears to be responsible for turning on a data tip:
% Redefine labels
h.DataTipTemplate.DataTipRows(1).Label = 'b'; % X
h.DataTipTemplate.DataTipRows(2).Label = 'a='; % Y
h.DataTipTemplate.DataTipRows(3).Label = 'L='; % Z
row = dataTipTextRow('DE76=',DE76(:));
h.DataTipTemplate.DataTipRows(end+1) = row;
% Show datatip
% Syntaxe: datatip(target,x,y,z)
datatip(h, h.XData(1),h.YData(1),h.ZData(1));
If this bit of code is still in your application, you can simply comment it out, or perhaps move it to where it should be (i.e., move it so that the data tip turns on when it should).
