How might one get a conditional display of tooltip or popup message from a rewritten view field?
You are actually on a good track - and you can use html in the no result text field. An easy solution to just attach the tooltip to the 'X's would be to add the needed info for tipsy there:

&lt;a class="tipsy-tooltip" title="My tool tip" href="#"&gt;X&lt;/a&gt;


In the Tipsy module settings you would need to add the appropriate selector in the form of: a.tipsy-tooltip. The selector does not need to be unique - you can use classes instead of ids. That way you can address multiple entries with just one selector. 

Selectors are not linked to the position in the table, but rather identify a particular tag. In this case the element the 'a' tag which wraps around X. If the table gets resorted, the tooltip is still attached to the Xs.



Edit 1

The Problem might just be your selector: a.views-field views-field-nothing. 

CSS classes are interpreted linearly and the order is important. In this case you are telling tipsy to look for a html element views-field-nothing which itself is nested unter a link a with the class views-field. If you look at the inspector though you will see that the actual mark-up is different and probably looks close to this one:

&lt;td class="views-field views-field-nothing"&gt;
    &lt;a class="tipsy-tooltip" title="My tool tip" href="#"&gt;X&lt;/a&gt;
&lt;/td&gt;


A link a nested in a element with the classes views-field and views-field-nothing. Tipsy can't convert the default tooltip to a tipsy tooltip because it doesn't find the link to start with.

The correct selector would look like this: .views-field.views-field-nothing a (The missing space between the first two classes is important, as are the dots before the names which indicate they are classes rather than html elements or ids. If you made a space between the first two, it would look for an a-tag nested in a element with the class views-field-nothing which itself is nested under the element with the class views-field.)

Since views-field is a class applied to all fields views outputs you can as well leave it out though and just write .views-field-nothing a

The Problem with views-field-nothing is that it applies to all views and not even just for fields where 'no result' applies - views also uses the same class for fields of the type custom text. To make sure you just target the links you want to turn into tooltips it is easier addressing them with a class on the link itself - e.g. with the a.tipsy-tooltip selector I suggested. It specifically looks for all links with the class tipsy-tooltip so tipsy can extracts their title attribute and uses it for its tooltip text. 

You should also pick the 'HTML Attribute' option in this case (Source: 'HTML attribute', Selector: 'title'). The only time you really need to use the 'Child Element' option is when you want to use HTML in the tooltip as you can't do that with the former. With the 'HTML Attribute' option tipsy uses whatever you put as the links title as the tooltip text - no extra classes needed.